I don't have a passport, but my driver's license has my marriage name and my birth certificate has my maiden name. We had a lot of trouble at the Delta counter trying to get our plane tickets. They asked me for my marriage license and I didn't have it. After a long wait and a lot of suspicious looks from the Delta people, they finally let us go.
Next time, I will have my marriage certificate just in case if I do not have a passport by then.
BTW -- we've gone away (same travel process) 2 other times since we've been married and I only had this problem this last time. Go figure.