How To Change Name On Southwest Airlines Get in touch with Southwest Airlines customer support to have your name changed on a ticket. Contact 1-800-I-FLY-SWA (1-800-435-9792) or go to a ticket counter for Southwest Airlines. You will have to present proof of the name change, such as a court order or marriage certificate. Modifications can also be made using the "Manage Reservations" section of the Southwest Airlines website. Depending on the kind of adjustment, there can be fees. To prevent any travel interruptions, make sure you finish this step plenty of time before your trip.