There is already a great answer about travelling with two passports. What happens if the spelling in the passports is slightly different (due to alphabet transliteration into English?)
Let say a person has citizenship from countries A and B. That person buys round trip ticket from A to B and back to A.
In theory that person should show the B passport when flying to country B and show the A passport when flying to A. This means the airline ticket spelling will mismatch one of the passports