It can be under your name or a name you choose! Some reservation offers already include the AppointmentTrader Transfer Service which will transfer the reservation in to your name. If its not included you can add it on after buying the reservation for a small fee. One thing on that though: As many reservations become available at last minute, taking a reservation in someone else name is quick and great for privacy. Most reservations on AT are listed with a virtual phone number, so all you need to do is present the phone number at the hostess stand and you are good to go!