I applied in under my maiden name passport. I sent everything with that passport number and name even after I got my married name passport. When I went to my interview I showed them my old (maiden name) passport then my new passport. They didn't even flinch. She just said "oh you just changed your name to your married name" and continued on. It's a very common thing. They took my new passport to put my visa in, completely seamless. Just make sure you have your passport you applied with that's most important.