she'll be able to file 90 days before the November green card date (sometime in July???) for her naturalization
so,, you can wait and ask for name change (if you want) in that process
depends on so many things like does she have state ID or driving license and need to change it there (for example)
is it urgent to change it?
Its not a problem to travel with mismatching documents- you simply need to bring proof of the mismatch. Specifically for your situation- your wife can travel with a passport issued in her married name (Mary Jones) and have a GC showing maiden name (Mary Smith) as long as she also shows her marriage certificate (proof of Mary Smith marrying and being able to use the name Mary Jones). Some marriage certificates state directly on them the new name, if it doesnt thats OK, it doesnt have to, it can still be used as a valid name change document. She will also need her NOA extension if her card is expired.
Now for the GC itself. You can send a letter to the service center you filed your 751 at requesting the GC be issued in her married name. The marriage certificate allows them to change her name. (I am assuming you are doing or attempting to do a very simple name change- ie her first name, middle name remains the same if she has one, and she will change from her maiden last name to yours right?) Theres no guarantee they will get your request or process it and issue the GC in the name you want. You can send it with a tracking number but when you mail stuff unsolicited it may not make its way into your file. If you get an RFE you can include the name change as part of your response. If there is an interview you can also request it there but they may tell you its too late/they cant change it at that point even though they could. If the GC is issued with the old name you will have to pay apx 600 to file the i90 at that point. You can also do as posted above and put it all off for now and make the change at citizenship filing.
Do not send another 751 with the name edited, just a basic letter asking for the change of name based on marriage.
Generally speaking for non citizens it all starts at USCIS. USCIS has a 'name on file' for you (e-verify/SAVE). You enter the system with the name on your passport (what they issue the visa using). You can update your name when getting an EAD issued or GC issued (with out having to pay extra cause you are paying for a card regardless of the name being changed or not if that makes sense). You can also update it at any time by paying and filing the i90. So its a good idea to try to take advantage of the times you are having cards printed to make name changes rather then paying a la cart. You should not file the i90 during ROC processing as they will not print you a replacement card since your card is expired due to ROC. So you would end up paying a lot of money simply to get the NOA for the i90 which would be useful if you actually lost the GC and needed to get a stamp (they wont stamp unless you show you filed i90 and the extension letter is only good when shown with the expired card)
So the typical process involves changing your name on various documents in a specific order. First is USCIS- then SSA (they will only issue you a SS card in the name on file according to USCIS)- then typically DMVs as most require you to show updated SS card along with verifying you with DHS-SAVE), then banks and employers once you have the updated DL.
I tried to go over a variety of information to give you the 'bigger picture'. If you have any additional questions or need additional clarification on any part- please post back.
