Instructions
Turn on your Xbox 360 and select the "My Xbox" tab.
Press "A" on your profile.
Select "Change Gamertag." As of July 2011, it costs 800 Microsoft Points, or $10, to change your gamertag.
Select "Enter New Gamertag" if you have a specific name you wish to change to. Select "Get Suggestions" to be shown random unused gamertag names. If the name you select is taken, you are prompted to select a new name.
Select "Yes" to permanently change your gamertag. The process takes a few minutes and, once finished, your new name is displayed on your profile.