Call you travel agent. If you booked your ticket through a travel agent you should let them handle name changes with the airlines. They should have experience dealing with similar situations, and can get in contact with the right airline representative. Airlines are usually unwilling to change names because of security issues, and a travel agents can help reassure an airline no such issue exist.
Read the fine print on your ticket or the airlines website. Knowing all the information ahead of time will make it easier to plead your case to the airline. If your ticket was non-refundable or non-transferable you will have a difficult time changing the name. If the flight is regional and has no restrictions you should be able to get the name changed. When visiting an airline's website look for the 'Ticketing," "Fare Info" or similar link. This will explain an airline's ticket policy. Many low-cost airlines will change a name for a fee. But many larger airlines will not. Delta states "tickets are valid for the named passenger only and are not transferable." American Airlines will only change a name for "spelling changes, changes to last names due to marriage or divorce and changes to prefixes."
Call the airline to change the name on your ticket. There are some circumstances -- marriage or divorce -- where airlines will change the name on a ticket, but other times, like international travel, where a name cannot be changed for any reason. Having a reason for needing to change a name on a ticket may help convince the airline.
Cancel your ticket reservation if you are not able to change your name. If the airline refuses to change the name on the ticket request a refund. Even if the ticket is non-refundable airlines will often give you a credit towards future air travel. In many instances, it is easier to cancel a ticket, and rebook with the new name.
