When we filled in the paperwork, we were scared that the embassy would get confused, so we filled in everything with my married name. However, being very recently married, I still had my passport and other documents at my maiden name.

On the day of my interview in Paris, after I was approved for getting the green card, the officer strongly advised me to get the documents in order (with my married name on them) and send them the new passport for them to stamp. This is for a really simple reason: the stamp or visa in your passport is named after the name used in the application.

If you keep your old passport with your maiden name and have a visa in it with your married name, you are risking to have problems at the customs during future travel. So make it simple, choose a name, stick with it and try to get your paperwork done on time for the interview.