name change on GC?

[inspektor]

When we married, my wife and I retain our last names. After that we came in US and get CGs on that names. Now she wants to change her born last name into mine. According this request, in our homeland she would get new Born Certificate (new issue from Local Authorities according our homeland laws). IS THIS DOCUMENT O.K. FOR REPLACING NAME ON GC IN US? (US claims that we need to subbmit court decision or marriage certificate.)

Thanks,