Citizen's change of last name (problems)

[Heroe 1]

Hi. I'm a F-1 student who recently got married to an American born citizen and applied for AOS already. I'm from Spain, so I happen to have two last names, that I have been using as a one in the US. Every time that I would have to fill any immigration/visa document, I would use First Second, because it's supposed to be the way to do it.

Even though I have used both of my Spanish last names as my 'American' last name, my idea was to eventually change the last name to only my first Spanish last name (because it's the one you usually use the most in my culture, and it's just more comfortable to only use one word instead of two).

Now, the problem. I sent all the AOS papers with my last name being First Second, because I wanted to be consistent. My wife just went the other day to get her social security card changed, and she got to have my first last name as her last name, as we both wanted. However, when she went today to change her driver license, they didn't let her change her last name to what her social security said, because in the marriage license my last name appears with the two words, first last name and second last name. So she HAD to have her license changed to my 'American' last name, two words. Now she has a different name in her license and in her SS, and we're pretty confused about what we can do about this.

Do I need to change my name first before she can change hers? In this case, I guess it would have to be once I got the GC and not before. Is there any other way that she can just change her last name to whatever she wants (only my first last name) instead of having to wait for me to change my name?

Thank you very much.