My advice: If the flight was just purchased yesterday, and the fare shown online now is the same as when purchased, just cancel, request a full refund, and rebook with the correct name. Southwest (by law) allows cancellation with full refund within 24 hours of booking. If it's too late, or if the fare has increased, or if EarlyBird Check-In was added to the itinerary, I second the advice above. Just be prepared to be patient, and HUTA (hang up, try again) if you reach a rep that is unable to help you. Good luck.
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