when you file your documents with USCIS use the last name that shows on your DL at that time, meaning if you went to the DMV and changed your name and got a new DL or ID card with your new last name than thats the one you should use (there is a place to put down your maiden name on the USCIS papers - its where they ask for other names that you have used)
it will be a good idea to update your new last name with SS, DMV for when USCIS runs the background check on you and updating you passport will save you time and headache in future travel.

