ryna

If you file the AOS forms in the married name, there is a space for "previously used names" aka your maiden name. I see you are adjusting from a J-1(?) with overstay but it is still based upon marriage to a USC so you will be including a copy of your marriage certificate, correct? That is sufficient justification to file under the new name.
As for the SS Card, it sounds like you'll have to wait to change it with the SSA until you receive your Green Card. My wife came over on a K-1 (financee visa) and if she didn't get her SS card within 75 days, they wouldn't have issued her a card until she received her GC either as she will be technically "out-of-status" after 90 days (while we await her AOS.)
That's not a big deal as while you are waiting on the GC, your passport matches your existing SS Card...

With the Green Card. File all of your AOS forms using your married name. The SS Card can be changed if you already have one (original card plus marriage license) or, in the worst case, after receiving the Green Card. You don't want to change it after receiving the Green Card or you will pay for a new one ($340, I think it is.)

I agree with the others. If you can do it now, do it now. You never know what night happen in the future.
And, Jim brought up a good point, also. I know that after only 2 months, my wife is getting bored with being what she calls a "non-person" here - can't work, can't learn to drive, can't take English classes, can't be added to bank accounts, can't travel (outside the U.S.), can't....

There is a way to do this without spending months and months apart. It's called "You visiting him during the K-1 or CR-1 process."
Consider yourselves lucky that he's even been allowed to visit and see the U.S. before making his decision to move here. That's far more than the vast majority of the world is allowed to do.
Do it the right way because the consequences of trying to take the short-cut are severe. And, an AOS denial through a VWP entry can NOT be appealed.

Remind me again how it's anyone else's business when/where some other couple decides to get married?

Remind me again how it's anyone else's business when/where some other couple decides to get married?

Remind me again how it's anyone else's business when/where some other couple decides to get married?

I would suggest that when you know the case has arrived at the consulate, that you download the Packet 3 from the website to be certain that your receive your appointment package (packet 4). The DS-2100, which is part of Packet 3, is the beneficiary contact information form. It asks for address, phone number, email, etc. so that the appointment package arrives at the correct location.
You could also try calling the Dept of State after you have received the NOA2 and your consulate case #. They won't know about your case before that. There's really no reason to change the beneficiary's address during the USCIS phase as all correspondence with them takes place after the NOA2 and NVC.
Good luck!

Ok, just looking for some advice here..
I filed our K1 petition back in mid-April (before I found VJ). It was received by VSC and accepted (NOA1) within a week. A couple days after receiving the NOA1, for some reason, I got nervous about filing on our own and wanted to have an attorney review it.
I did, and he looked at what I had filed and told me, "It looks great and is the same as we would have filed. I could take your $$ but, to be honest, you've already done my job." I thanked him for his honesty, took his card for future reference, and left.
Now, I'm starting to wonder if it's getting close to "future reference" time. If our petition passes the 5-month mark, and I have to contact USCIS and/or my Congressman and Senators, is it worth having an attorney do so? Is there any advantage whatsoever? Or, should it be reserved for, God forbid, if the visa is denied (if we ever get to the embassy) and we need to appeal, etc.?
Has anyone ever brought an attorney on-board well after filing with any success?
I'm trying not to run every conceivable scenario through my head but sometimes it's difficult not to...

We all know how difficult it is to have to wait to be with our loved one so I'm not trying to sound harsh, either, but why doesn't he just visit you during the wait?
It's the ONLY option available to the majority of us. Remember, at least you have a chance of being allowed a visit before receiving your visa. From what I understand, being turned around at the border (for reasons of possible immigrant intent) won't affect your K-1 visa, so you can always try. And, if you don't get in now but have ever had the opportunity to visit him in the U.S. before the K-1 petition was filed, you're already more fortunate than most.

Best of luck!