The quick answer is yes. You’ll likely have to if you decide to plan a honeymoon. I’ve flown with my maiden name passport two times now. There first was right after we got married for our honeymoon. There’s no time to change your passport to your married name before the honeymoon so simply book your honeymoon flights with your maiden name and you’ll be fine.
But what if you already changed your social security card, license, bank accounts, award accounts, etc.? Can you still fly with your maiden name passport? I recently went to Peru using my maiden name passport even though my name is changed everywhere else. We booked this trip nine months earlier (three months before we got married). Since we were hiking the Inca Trail, we had to provide our passport numbers for the permits at the time of booking. Similar to the first example, all you have to do is make sure your name on your passport matches your airline tickets. For those with Global Entry, this should continue to work until you update your passport. Then you’ll have to go through the process of updating Global Entry as well. Isn’t changing your name fun?