Instructions
Select "My Xbox" from your console's menu system.
Select "Change Gamertag" and "Enter New Gamertag" from the menus on screen. This opens the interface that allows you to specify a gamertag for your Xbox 360 console. This one gamertag will be used across all games you play online, no matter who made them or when they were released.
Put your clan tag at the front of your Xbox 360 gamertag, if applicable. If you are a part of a clan or other group of people who play the same games with one another, insert the tag for your clan prior to your actual user name. This allows the people you play with to immediately know what clan you are a part of.
Choose a name that doesn't allow people to easily figure out your true identity. For safety purposes, don't use your first and last name or any combination of your real name as your gamertag. Use a pseudonym, nickname or any other name that allows you to successfully hide behind your virtual identity.
Highlight and select the "Yes, use this gamertag" option to save your changes and input your gamertag onto your Xbox LIVE account.