For citizens of the United Kingdom: If you have applied for a Post-dated passport that will not be valid until after your marriage, you will not be able to apply for ESTA using that passport until the day when the passport becomes valid. We recommend you make arrangements to apply between the ceremony and going to the airport. The application process is not complicated and should take no more than 20 minutes.
For travelers from other Visa Waiver Program (VWP) countries: If you have received approval to come to the U.S., but then change your name as a result of marriage, divorce, or other legal proceeding, you must re-apply and pay for a new ESTA authorization. We suggest applying 72 hours before you travel, we understand that this is one of those circumstances that can make it impossible to do so, but our system will accommodate your situation.
If you have a passport under one name, but your name has changed since it was issued, you can apply for ESTA using your old passport number and new name. You may also travel with a ticket issued in your new name and the passport in your old name, but we strongly recommend you bring a copy of your marriage license, divorce decree or other legal document showing the connection between your new name and the one on your passport.