In my case, the only thing I was waiting on to send in my application was the same thing I would need to change my name in the U.S. - my marriage certificate. It would be possible to do that, I guess, but then you're adding time onto the application process because you'd need to wait for the updated passport to arrive, and you have to send in your passport when you do the name change, which could be a problem if you wanted to travel during that window. I decided not to mess with changing my name until I'm done with everything just to simplify the process. I was worried that it would end up messing with the length of time of the background check, as well. Just my two cents.