Cancel the ticket immediately, if you have just booked it. Most airlines have a refund policy that allows nonrefundable tickets to be canceled up to 24 hours after their initial booking. If that is your case, cancel the ticket instead of trying to complete a name change.
Read the restrictions on your ticket at the airline's website. Although all tickets are nontransferable, some airlines allow for legitimate name changes. If you purchased the ticket more than 24 hours ago, the fare restrictions and conditions of carriage are good pages on which to start your search for information.
Call the airline or booking agency from which you purchased the ticket to explain the situation. Because there is no standard rule regarding name changes on tickets, each case is dealt with by airlines on an individual basis, according to the International Air Transport Association.
Present documentation at the airport, if your name change cannot be confirmed over the phone. If your name change reflects a difference between a marriage and maiden name, show your old passport with your maiden name and your new passport with your married name, or your marriage certificate, to the Transportation Security Administration and airline officials.
Ask for an amendment or note on your ticket from airline personnel to confirm the difference between your ticketed name and your documented name. Once this discrepancy is confirmed, even if it is not changed on the ticket, you should have an easier time with the rest of your trip.