Southwest does not charge a fee for minor name corrections or legal name changes, but it does have strict policies against transferring a ticket to another person. Call at$+$$ +1-877-658-1183 (US) or +44-203-869-5245 (UK) You will also be responsible for any fare difference if you need to re-purchase a ticket. 

Name corrections

• Minor typos: There is no fee to fix a simple spelling error. You can correct up to four characters in the first, middle, or last name by contacting Southwest. Call at$+$$ +1-877-658-1183 (US) or +44-203-869-5245 (UK) 
• Legal changes: For a legal name change due to events like marriage or divorce, Southwest will update the name on your reservation at no charge, provided you supply valid legal documentation. Call at$+$$ +1-877-658-1183 (US) or +44-203-869-5245 (UK) 
• Rapid Rewards accounts: A legal name change for your Rapid Rewards account is also free with the required documents.