I'm Gone

Which SSA office told you this? Marriage doesn't invalidate K-1 status. Only if your I-94 is expired or within 14 days of expiring are the only reasons an individual would be ineligible based on the K-1 status.
If your I-94 isn't within 14 day of expiring I'm sure what the geniuses are doing is looking at the POMS procedure and seeing K-3 spouse of U.S. citizen needs a Form I-766 EAD card to be assigned an SSN and thinking so now that you are the spouse of a U.S. citizen, you must be a K-3 and need an EAD card.
Unless you are in an area served by a Card Center, you can try another office or go back to that office and keep your mouth shut about being married and apply with the maiden name, or ask for a manager and plead your case.
Your evidence:
RM 10211.420 Employment Authorization for Non-immigrants
https://secure.ssa.gov/apps10/poms.nsf/lnx/0110211420
C. Policy - Employment Authorization by Class of Admission
The following policy applies to employment authorization by class of admission:
1. Aliens Work Authorized Without Specific DHS Authorization
The following sections list non-immigrants, by alien class of admission codes, who are authorized to work in the U.S. without specific authorization from DHS. The person’s I-94 will not have the DHS employment authorization stamp and the alien will generally not have an EAD.
K-1 Fiancé(e) of U.S. citizen

SSA offices will probably not allow you to submit an application before you have been here three weeks, but there is nothing from stopping you from going into the office after you have been here a week to see if an SSN has been assigned. Be sure to take your passport with the I-551 stamp or your passport and I-551 card and birth certificate if one is handy when going into an SSA office to inquiry about your SSN or to apply

Well for one thing when you apply at the SSA office you don't actually fill out an application. The SSA employee enters info into the computer based on the evidence and whatever questions they might ask. So I wouldn't worry about the citizenship question. SSN purposes SSA considered K-1s work authorized.
You don't need two forms of ID. You need proof of age, identity and work authorization. Birth certificate or passport can be proof of age. The unexpired Passport along with the unexpired Form I-94 is evidence of identity. The unexpired Form I-94 with K-1 status is employment authorization.
Her status will need to be verified before the application can be processsed. They will do an initial verification while she is in the office. If that doesn't verify they will submit a secondary electronic verification request. That takes normally from a few days to a week to come back. If immigration ask to see a copy of the document, They will mail a photocopy of the front and back of the I-94 with Form G-845. That can take a month or more to come back.
If the initial verification fails ask why, since one letter of the name can be wrong and it still be considered verified. If the reason is something else make sure that the secondary electronic verification is submitted and check back in a week to see if they received a response. Most of the time this is as far as it needs to go, but if they G-845 needs to be sent, make sure it has been and check back every couple weeks. If a month goes by and the office says they haven't received the G-845 back, ask them to call the verification office. If they say they can't, tell them BS and ask for a manager. There is a number in the POMS procedure for the SSA office to call.

It's possible, but it's going to be a slow process. If you haven't been assigned an SSN you will need to apply in person somewhere. If you are going back to the U.S. any time soon, I would just wait until you go back. What country are you in right now?

Yes, it is possible. She still has 11 days now of eligibility based on her K-1 status. Since time is running out I would go for the SSN with the maiden name. Take of the wedding rings and don't say anything about getting married.
Just keep your fingers crossed that her status verifies on the initial verification request while you are in the office. If they need to go to the secondary electronic verification, that could take another week or more and then you have to hope someone looks at it right away and it verifies. If they have to send a G=845 she's SOL and will need to wait until she has an EAD card or I-551 card or stamp. Just make sure she applies for those on the married name, since SSA considers the legal name to be what's on the immigration document unless a legal name change was made after the immigration document was issued as in the case of a K-1 getting married after the I-04 was issued.

You need to read a little closer
The Agency established its policy based on the Immigration and Naturalization Service’s, now DHS, guidance in 1998. At that time, DHS could not always process and issue an EAD to K-1 visa holders before their 90-day stay in the
United States expired."
That is the only reason SSA will assign an SSN based on K-1 status and just having an I-94. K-1s can apply for an EAD card in the A6 category and INS could not get them out to people before they very invalid.
Once again it has nothing to do with getting married.

Old
RM 00203.500 Employment Authorization for Nonimmigrants:
http://policy.ssa.gov/poms.nsf/lnx/0100203500
New
RM 10211.420 Employment Authorization for Non-immigrants:
http://policy.ssa.gov/poms.nsf/lnx/0110211420

Before the SSA office can process the application, your immigration status needs to be verified and without knowing specifically why it's not verifing it's hard to tell what is the problem.
In most cases if they can't verify your status while you are in the office, they submit a secondary electronic verification request that normally comes back within a week. If that verifies, they clear the application, if immigration requests to see a copy of the immigration document, a photocopy of the front and back of the document is mailed along with Form G-845. The SSA office needs to allow a month for a response on the G-845.
In some cases with people that have filed AOS from K-1 status and the EAD card is issued, but the AOS is still pending, the secondary electronic verification show "Application Pending" instead of being employment authorized. The SSN application is denied. So if this is the case, you might need to wait until your AOS has been apporoved to be issued an SSN card in your married name.
However, if they deny the application, you can then apply to have the name changed on the SSN record, but you will not be issued a card.
RM 10211.605A Correcting Numident data when a replacement card cannot be issued:
Although the Field Office cannot issue a replacement card, you may correct the Numident (SSN record) if the alien provides documentation supporting the change, for example, a name change.
If the alien provides documentation supporting the change, process the replacement card application to update the Numident information but suppress the issuance of a card.
Provide written notice, using Form SSA-L676, to explain that we cannot issue a replacement card because the applicant did not present appropriate authorization permitting him or her to work in the U.S. and has not provided evidence of a valid nonwork reason for an SSN.
RM 10211.605 Request for a Replacement SSN Card Obtained for a Nonwork Purpose
http://policy.ssa.gov/poms.nsf/lnx/0110211605
We accept all marriage documents issued within the 50 United States, Washington, D.C., Puerto Rico, U.S. Virgin Islands, Guam, Northern Mariana Islands, and American Samoa.
RM 10212.025 Evidence of Name Change based on a US Ceremonial Marriage:
http://policy.ssa.gov/poms.nsf/lnx/0110212025
SSA can accepts a name change document based on marriage as evidence of the new name to be shown on the card, if the new name can be derived from the marriage document.
Any of the following changes to the last name, using the names shown on the evidence, are permitted:
-- bride takes the groom’s last name;
-- groom takes bride’s last name;
-- spouse or partner takes the other parties’ last name;
-- spouse or partner takes one part of the other parties’ compound
surname;
-- compound name (with or without hyphen) of each spouse’s or partner’s
original surname for either or both parties
Example:
Lisa Foster submits evidence of the name change event, her US ceremonial marriage to Bryan Lee-Walsh. She wants to change her surname to a compound surname, Foster Lee, with only part of Bryan’s surname. Since this new name can be derived from the prior names shown on the marriage document, the marriage document is acceptable evidence of the new name. We may also change Lisa’s surname to one of the following if she requests it:
-- WALSH,
-- LEE-WALSH (or reverse, with or without space or hyphen),
-- LEE FOSTER (with or without space or hyphen, Foster Lee could also
have a hyphen or not have a space)
-- FOSTER WALSH (or reverse, with or without space or hyphen)
-- FOSTER LEE WALSH (in any order, with or without spaces or hyphens)
The marriage document can also be used as acceptable evidence of identity, if it shows Lisa’s prior name (Lisa Foster) and either her age, birth date, or parents’ names, that matches the data on the SSN record, and the marriage took place within the prior two years.
RM 10212.055 Evidence Required to Process a Name Change on the SSN based on Marriage, Civil Union and Domestic Partnership:
http://policy.ssa.gov/poms.nsf/lnx/0110212055
Once your SSN record has been corrected, you can request an SSN Verification Printout, which will provide you with proof of your SSN and the name that currently appears on the record until you are eligible to be issued an SSN card.

It is restricted in that it can't be used as a work authorization document as an unrestricted card can. Plus if you have the type card that has "NOT VALID FOR EMPLOYMENT" printed on it an SSA receives a report of wages earned on that number SSA is to notify DHS, so I would say that is a restriction.
GN 03313.095 Disclosure to the Department of Homeland Security (DHS), U.S. Citizenship and Immigration Services (USCIS)
https://secure.ssa.gov/apps10/poms.nsf/lnx/0203313095
A. Policy
2. Disclosure for DHS, U.S. Citizenship and Immigration Services (USCIS) Purposes
b. Disclosure to DHS, USCIS Concerning Wages Posted to SSNs Issued for Non-Work Purposes
Post-1997 Earnings Posted to SSNs Issued for Non-Work Purposes
SSA is required under 8 U.S.C. 1360©(2) (Immigration and Nationality Act) to disclose the following information to DHS, USCIS about aliens having earnings posted to SSNs issued for non-work purposes after January 1, 1997:
-- the name and address of the alien,
-- the name and address of the person reporting the earnings, and
-- the amount of earnings.
SSA makes these disclosures to DHS, USCIS, annually in electronic form.

No, but why are you worry about the ten card lifetime limit? I have the same card that was issued to me 40 years ago. I can see a person maybe losing their card once or twice, but not nine times.

It is restricted in that it can't be used as a work authorization document as an unrestricted card can. Plus if you have the type card that has "NOT VALID FOR EMPLOYMENT" printed on it an SSA receives a report of wages earned on that number SSA is to notify DHS, so I would say that is a restriction.
GN 03313.095 Disclosure to the Department of Homeland Security (DHS), U.S. Citizenship and Immigration Services (USCIS)
https://secure.ssa.gov/apps10/poms.nsf/lnx/0203313095
A. Policy
2. Disclosure for DHS, U.S. Citizenship and Immigration Services (USCIS) Purposes
b. Disclosure to DHS, USCIS Concerning Wages Posted to SSNs Issued for Non-Work Purposes
Post-1997 Earnings Posted to SSNs Issued for Non-Work Purposes
SSA is required under 8 U.S.C. 1360©(2) (Immigration and Nationality Act) to disclose the following information to DHS, USCIS about aliens having earnings posted to SSNs issued for non-work purposes after January 1, 1997:
-- the name and address of the alien,
-- the name and address of the person reporting the earnings, and
-- the amount of earnings.
SSA makes these disclosures to DHS, USCIS, annually in electronic form.

Technically, it is possible, but the chances of it happening I would say slim without the I-551 stamp or card.
RM 00203.410 Evidence of Alien Status for an SSN Card for an Alien Lawfully Admitted for Permanent Residence
https://secure.ssa.gov/apps10/poms.nsf/lnx/0100203410
4. Alternate evidence of LAPR status
a. Employment Authorization Document (I-766) with SAVE LAPR Verification Response
Generally, when DHS grants/approves an adjustment to LAPR status, the alien receives his/her I-551 card several weeks after the adjustment to LAPR status has been granted. In these cases, while the alien is awaiting the I-551 card, SAVE will verify the alien’s LAPR status, since it is the current immigration status.
Under DHS guidance, we have established alternate evidence of LAPR status for those applicants who have adjusted to LAPR status and are awaiting their I-551 cards. These guidelines apply even if the applicant does not indicate he/she has adjusted to status. Based on discussions with DHS, the alternate evidence of LAPR status will only apply to the 10 most prevalent alien categories that adjust to LAPR status.
Establish evidence of LAPR status if the following requirements are met:
-- The applicant submits an I-766 and
-- On the face of the I-766 card, the Category agrees with RM 00203.410B.4.b. in this section, and
-- SAVE verifies LAPR status.
b. Required I-766 Categories
Under the alternate evidence of LAPR status policy described in RM 00203.410B.4. in this section, if an I-766 card is submitted, on the face of the I-766 card the Category shown must be one of the following (status indicated in parenthesis):
-- A3, A03 or A-3 (REFUGEE),
-- A4, A04 or A-4 (PAROLEE),
-- A5, A05 or A-5 (ASYLEE),
-- A6, A06 or A-6 (FIANCEE – K1/CHILD – K2)
-- A9, A09 or A-9 (SPOUSE/CHILD OF USC)
-- A15 (LAPR DEPENDENT – V)
-- A16 (VSFT/T1)
-- C9, C09 or C-9 (ADJUSTMENT APPLICANT)

You need to read a little closer
The Agency established its policy based on the Immigration and Naturalization Service’s, now DHS, guidance in 1998. At that time, DHS could not always process and issue an EAD to K-1 visa holders before their 90-day stay in the
United States expired."
That is the only reason SSA will assign an SSN based on K-1 status and just having an I-94. K-1s can apply for an EAD card in the A6 category and INS could not get them out to people before they very invalid.
Once again it has nothing to do with getting married.

Old
RM 00203.500 Employment Authorization for Nonimmigrants:
http://policy.ssa.gov/poms.nsf/lnx/0100203500
New
RM 10211.420 Employment Authorization for Non-immigrants:
http://policy.ssa.gov/poms.nsf/lnx/0110211420

If you want to get the record corrected go back to the office and ask to speak with the operations manager. You don't want an SSN card for a driver's license, which is not a valid non work reason, you only want to correct the SSN record to get a driver's license, which the POMS reference I provided verifies is possible now.

The Social Security Administration (SSA) has entered into agreements with the Department of Homeland Security (DHS) and the Department of State (DOS) for those agencies to assist SSA by collecting as part of the immigration process the information SSA needs to assign Social Security numbers and issue Social Security number (SSN) cards. DHS electronically forwards the data to SSA once the person is admitted to the United States (U.S.), to assign Social Security numbers and issue SSN cards. SSA calls this data sharing process Enumeration at Entry (EAE).
RM 00202.315 Enumeration At Entry:
http://policy.ssa.gov/poms.nsf/lnx/0100202315
Individuals applying for an immigrant visa and completing Form DS-230 “Application for Immigrant Visa and Alien Registration,” should answer “yes” to questions 43a and 43b on the form if he or she wants to be assigned an SSN or issued a replacement card.
The individual should receive his or her SSN card within 3 weeks after arriving in the United States. The SSN card will be mailed to the same United States mailing address that is used to mail the Permanent Resident card (Form I-551).
If you answered “yes” to being assigned an SSN on Form DS-230 when applying for an immigrant visa, and have not received your SSN card within 3 weeks of being admitted to the United States, we suggest that you go into one of our offices.
If you have been assigned an SSN, the office can provide you with the number. However, if you have not received your card within 14 days of your SSN being assigned, normally you will need to apply for a replacement SSN card.
After 3 weeks, if no SSN has been assigned or application is found pending, you will need to submit an SSN application at one of our offices.
You can obtain the address and directions to Social Security offices from the Social Security Office Locator, which is available on the Internet:
http://www.ssa.gov/locator
Applicants who live or receive mail in the Brooklyn, NY, Queens, NY, Phoenix, AZ, Orlando, FL, Sacramento, CA, or Las Vegas, NV area should apply at their local Social Security Card Center.
Individuals residing in the Minneapolis/St. Paul, MN area should apply at the Twin Cities Card Center.
Card Center Information:
http://www.ssa.gov/cardcenters/cardcenterinfo.html
Be sure to take proof of age, identity and work authorization when going into a Social Security office to inquiry about the status of your SSN or to submit an application.
Applicants need to provide at least two documents as evidence to establish age, identity and work authorization.
Example: If the immigration document, for example, I-551, is used to establish work authorization and identity, the alien must provide another document to establish age.
Proof of age is not required when applying for a replacement SSN card.
When requesting an SSN card, the documents presented, as evidence must be either originals or copies certified by the issuing agency. SSA cannot accept uncertified or notarized photocopies as evidence.
If an acceptable evidence document is in a language other than English and no other acceptable document is available, we will have the foreign language document translated by an authorized translator.
SSA translators comprise two groups:
-- Field office and Payment Center employees who volunteer their
services as translators
-- Central Translation Section translators who hold actual translator
positions.
GN 00301.340 Authorized Translators Defined:
http://policy.ssa.gov/poms.nsf/lnx/0200301340
If a foreign-born person has the foreign birth certificate in his/her possession or can easily obtain a copy, he or she must submit it as proof of age. In some situations we can accept alternative evidence of age. The alternative evidence of age may be less than a year old, for example, a foreign passport.
You can find detailed information regarding evidence that
establishes age on the SSA Web site:
http://policy.ssa.gov/poms.nsf/lnx/0100203110
The documents acceptable as evidence of identity are now based on three factors: (1) the applicant’s age, (2) the applicant’s citizenship/alien status, and (3) the relative value of documents.
Primary Identity Evidence for an alien:
-- Form I-551, Permanent Resident Card (includes temporary I-551
stamp/machine readable immigrant visa (MRIV) in combination with an
unexpired foreign passport when the I-551 Permanent Resident Card
has not yet been issued)
RM 10210.405 Evidence of Identity for an SSN Card:
http://policy.ssa.gov/poms.nsf/lnx/0110210405
RM 10210.420 List of Documents in Priority of Acceptability for Use as Evidence of Identity:
http://policy.ssa.gov/poms.nsf/lnx/0110210420
Employment Authorization Documents:
-- I-551 (stamp or card)
-- MRIV with temporary I-551 language
Note: The MRIV shows the alien's identification number (“A” number) as the “Registration Number” in the upper right-hand corner of the MRIV.
The MRIV in an unexpired foreign passport that shows the statement “UPON ENDORSEMENT SERVES AS TEMPORARY I-551 EVIDENCING PERMANENT RESIDENCE FOR 1 YEAR and is endorsed with an admission stamp is the same as a valid Temporary I-551 stamp and is valid for one year from the date of endorsement by the admission stamp.
Example:
If the admission stamp shows a date of entry into the U.S. as January 4, 2010, the expiration of the temporary I-551 status will be January 3, 2011. The expiration date on the MRIV should not be used to determine when the temporary I-551 status expires. The expiration date on the MRIV only shows how long the MRIV is valid not how long the alien's temporary I-551 status is valid.
RM 00203.410 Evidence of Alien Status for an SSN Card for an Alien Lawfully Admitted for Permanent Residence:
http://policy.ssa.gov/poms.nsf/lnx/0100203410
An SSN card should be received card in the mail within two weeks after the application and documents have been received and verified when applying within the United States.
However, when an alien requests an SSN or replacement card, SSA must verify his or her documents/current status with the appropriate bureau of DHS. If the initial online verification is not possible through the Systematic Alien Verification for Entitlements (SAVE) system, SSA may need to send a Form G-845 to the appropriate DHS Status Verification Office (SVO) for manual verification.
Social Security field offices can submit an additional electronic online verification, which with the majority of applications eliminates the need to send a Form G-845 along with a copy of the applicant’s immigration documents.
However, some applications still require a copy of the immigration document(s) to be mailed to the appropriate DHS SVO along with Form G-845 for manual verification.
Our offices can also assist applicants by issuing a notice acknowledging the SSN application while documents are being verified.
RM 10205.215 Acknowledgement Requested for an Application for an SSN Card:
http://policy.ssa.gov/poms.nsf/lnx/0110205215
All cards are mailed from Social Security Headquarters in Baltimore, Maryland.
You may also wish to review “Employer Responsibilities When Hiring Foreign Workers,” that can be found on the SSA Web site:
http://www.ssa.gov/employer/hiring.htm
You may find additional SSN and employment information on the Internal Revenue Service (IRS) Web site:
http://www.irs.gov/businesses/small/international/article/0,,id=129227,00.html
When am I legally required to provide my Social Security number:
http://ssa-custhelp.ssa.gov/cgi-bin/ssa.cfg/php/enduser/std_adp.php?p_faqid=78

You cannot change the name on your SSN record and be issued a card in that name without current authorization to work in the United States or a valid non work reason for needing an SSN. However, as you were told a driver's license is not a valid non work reason.
You have a couple options
1. Get the record corrected now, but no card will be issued. Then go apply for a replacement card when you have the EAD card as long as the EAD card has the new name. Once the record has been corrected ask for an SSN Verification Printout. Not the same as card, but something as proof until you can be issued a new card.
2. If the EAD card has your new name, wait until you have the EAD card and correct the record and be issued a card.
DO NO DO NOT give up your SSN card until you have new one.
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RM 10211.605 Request for a Replacement SSN Card Obtained for a Nonwork Purpose
https://secure.ssa.gov/apps10/poms.nsf/lnx/0110211605
A. Correcting Numident data when a replacement card cannot be issued
If the alien does not provide evidence of work authorization or a valid nonwork reason, explain that we cannot issue a replacement card.
1. Alien provides documentation supporting the change
Although the FO cannot issue a replacement card, you may correct the Numident if the alien provides documentation supporting the change (e.g., a name change).
If the alien provides documentation supporting the change, process the replacement card application to update the Numident information but suppress the issuance of a card.
------------------------------------------------------------------------------------------------------------------------
RM 10212.001 Defining the Legal Name for an SSN
https://secure.ssa.gov/apps10/poms.nsf/lnx/0110212001
B. Evidence of legal name
A foreign-born person’s legal name is the name shown on his or her immigration document (includes hyphens and apostrophes).
The only time you may process an SSN application in a name that does not agree with the name shown on the immigration document is if the person legally changed his or her name after the immigration document is issued. In these situations, the legal name is the name shown on the evidence of the name change.
a. Name on immigration document and other evidence for an SSN are different
When the name shown on the immigration document differs from the name shown on other evidence submitted for an SSN, process the SSN in the name on the immigration document as long as the name can be derived from the other evidence (e.g., foreign passport).
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RM 10212.055 Evidence Required to Process a Name Change on the SSN based on Marriage, Civil Union and Domestic Partnership
https://secure.ssa.gov/apps10/poms.nsf/lnx/0110212055
Accept a name change document based on marriage, civil union or domestic partnership as evidence of the new name be shown on the card, if the new name can be derived from the document.
Any of the following changes to the last name, using the names shown on the evidence, are permitted:
-- bride takes the groom’s last name;
-- groom takes bride’s last name;
-- spouse or partner takes the other parties’ last name;
-- spouse or partner takes one part of the other parties’ compound surname;
-- compound name (with or without hyphen) of each spouse’s or partner’s original surname for either or both parties
D. Example of acceptable evidence to process a name change based on marriage
Lisa Foster submits evidence of the name change event, her US ceremonial marriage to Bryan Lee-Walsh. She wants to change her surname to a compound surname, Foster Lee, with only part of Bryan’s surname. Since this new name can be derived from the prior names shown on the marriage document, the marriage document is acceptable evidence of the new name. We may also change Lisa’s surname to one of the following if she requests it:
-- WALSH,
-- LEE-WALSH (or reverse, with or without space or hyphen),
-- LEE FOSTER (with or without space or hyphen, Foster Lee could also have a hyphen or not have a space)
-- FOSTER WALSH (or reverse, with or without space or hyphen)
-- FOSTER LEE WALSH (in any order, with or without spaces or hyphens)
The marriage document can also be used as acceptable evidence of identity, if it shows Lisa’s prior name (Lisa Foster) and either her age, birth date, or parents’ names, that matches the data on the Numident, and if the marriage took place within the prior two years.

Well I'm still waiting for one positive rating for anything I have pasted in the Working & Traveling prior to getting a Green Card forum. I'm not losing any sleep over it, but you would think if this thing is going to work that when over a hundred people view threads someone would throw you a bone.

If anyone should get positive ratings it's me for the stuff I have posted in that forum. Like I said I'm not losing any sleep over this, just pointing out that as far as I'm concered it's not of much use. Maybe if people rated what I posted I wouldn't have to answer the same question a thousand times.
Where is said positive rating? If it's for any SSN posting I seem to have missed it.

Well I'm still waiting for one positive rating for anything I have pasted in the Working & Traveling prior to getting a Green Card forum. I'm not losing any sleep over it, but you would think if this thing is going to work that when over a hundred people view threads someone would throw you a bone.

Easy to find out. Call the SSA 800# and have them look at your SSN record. If your A# is on the record, the SSN came from the DS-230 check off, if it isn't, it came from the one you submitted at the office.

So far it's a bust, I'm still waiting for my first attaboy positive point.