Sorry, but no airline allows the name on a ticket to change. Also, no one can fly on another person's ticket. Your best bet is to cancel the ticket of the person who won't fly (with that person getting a travel credit for a future flight that must be completed within one year of the date the original ticket was bought). You might want to wait until near the date of travel to do that in case the situation again changes. Also keep looking at ticket prices. They sometimes come down. If so , that'd be your chance to buy a ticket for the one year old.
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