To change the name on a flight ticket you should always contact the airline or travel agent you booked with as soon as you realise the name change is needed. This is because many airlines will have a cut-off point for name changes (generally up to 24 hours before the flight).

Changing a name on a plane ticket is one of the most difficult and potentially expensive administrative tasks in travel, as most tickets are strictly non-transferable. If you have a minor typo (1-3 characters), most airlines will correct it for free or a small fee, provided you call their customer service line and it doesn't change the identity of the passenger. However, for a major name change—such as after a marriage or divorce—you must usually provide legal documentation, like a marriage certificate, and many airlines will require you to "cancel and rebook" the ticket at the current market price, which can be thousands of dollars. It is important to note that you cannot change the name to a completely different person; this is a security measure to prevent ticket scalping. If you booked through a third-party site (like Expedia), you must contact them first, though they often refer you back to the airline. The best advice is to triple-check the name against your passport before clicking buy, as once the PNR is issued, the name is essentially "locked" into the airline's security manifest.