Southwest Airlines does not permit full name change, just minor change of names. In case of a minor spelling error, you may call Southwest Customer Service and ask them to make an amendment. They can request a copy of the ID to confirm the appropriate name. Major changes, such as transferring a ticket to another person are not possible at Southwest and thus you need to cancel the old ticket and re-book anew. The positive bit is that Southwest airlines name change does not impose change fees, and thus, you can cancel and get the travel credit reused with the right name. Always make sure to confirm your details before booking.