Instructions
Turn on your Xbox. Wait for the Xbox logo to appear on your screen.
Sign-in to Xbox Live. Input your current account information -- including the password -- if prompted.
Go to the My Xbox Channel. Choose "Change Gamertag."
Type your original Xbox Live account gamertag into the field. Hit "Enter" when done.
Wait for the system to check the availability of your name. If the name has not been cleared yet -- or has been taken by another user -- you will have to choose something different.