If she still has her SSN card DO NOT DO NOT give it up until she has a replacement.Applying before getting married will cause less hassles, but as long as the K-1 hasn't been here 76 days, getting married shouldn't matter and I would ask to see the office manager to make them accept the application and have immigration make the decision.
If the marriage certificate has her age or date of birth, that along with her I-94 and passport should be all she needs to be issued an SSN card in her married name at this point.
RM 00203.210 C. Procedure - Immigration Document as Evidence of Legal Name:
When an alien applies for an SSN card, we presume the name on the immigration document is the legal name unless the applicant presents evidence of a legal name change, e.g., marriage, which occurred after the immigration document was issued.
RM 00203.210 Changing Numident Name Data:
http://policy.ssa.gov/poms.nsf/lnx/0100203210RM 00203.735 Applicant Has Changed His/Her Name but Initial Verification Results Show Old Name
In some cases, the applicant may have changed his/her name after DHS issued the immigration document (e.g., he/she has married and is now using the spouse's last name) but does not present an immigration document showing the new name. In these cases, the DHS system reflects the new name only when the person provided the name change information to DHS and requested to have his/her immigration record changed to show the new name. When the initial verification results shows the old name that is shown on the immigration document presented and not the new name on the name change document presented, do not consider this a name discrepancy for enumeration purposes.
If the office manager still gives her a hard time point out that she can still correct the name on the SSN record.
RM 00203.510 D4 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 no replacement card can be issued.
Although a replacement card cannot be issued, the Numident can be corrected if the alien has provided documentation supporting the change, e.g., a name change.
If the alien provides documentation supporting the change, process the SS-5 to update the Numident information but suppress the issuance of a card.
RM 00203.510 Alien without Work Authorization - Nonwork Need for an SSN:
http://policy.ssa.gov/poms.nsf/lnx/0100203510#D4Once the SSN record has been corrected, she can request an SSN Verification Printout, which will provide proof of her SSN and the name that currently appears on the record until she is eligible to be issued an SSN card.
RM 00202.320 Issuing Numidents and SSN Verification Printouts:
http://policy.ssa.gov/poms.nsf/lnx/0100202320