In our case the new name *was* on my wife's green card. When we applied for her adjustment of status, we put the new name on part 1 of the I-485, and also on the G-325A forms, with her old name in the "All Other Names Used" blank on the G-325A. By adjustment of status time, she already had a social security # in her new name, as we had applied for that the week after we were married. The I-485 / I-864 / I-765 turned out to be the most complicated and intrusive set of government forms I have ever had occasion to complete. But we got it in on time. Her card arrived only 3 months! There was just one RFE - she had to get another physical.

Dale.