In flying away, the most important thing is that first you must ask about a name change on flight ticket according to flight ticket policy. Airlines vary differently while changing and changing names. Some do not abide by minor changes like proper spelling well done for peanuts or for nothing. But to change the entire name, i.e., a court order change of name, would be in a different form and another, indeed perhaps another offence.
Ring their customer helpline or go on to their website and get them to have you practice saying out what they would like you to say and what documents you would need to produce. Each of them has a specific page for name change, and hence reading between the lines must be something to investigate.
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