If your drivers license has your married name, use that to get through Security and that should take care of the TSA.
Checkin and the rest should be OK with your marriage license in addition to your passport, though that totally depends on who you get. Entering whatever country you are entering won't usually ask to see your ticket, so again they probably won't even see a name difference.
Of course, it depends on the mood of the person behind the counter when you check in.
Not sure how easy it will be to get through Immigration on the way back home with the name difference, that's where I think you may have some issues.