Instructions
Press the Xbox 360 ̶0;Guide̶1; button and press your controller's ̶0;X̶1; button. Select ̶0;Yes, Sign Out̶1; to sign out of any account you are currently signed into.
Press the Xbox 360 ̶0;Guide̶1; button again. Highlight ̶0;Recover Gamertag̶1; on the Xbox 360 home menu and press the ̶0;A̶1; button.
Confirm that you want to recover your Gamertag by pressing the ̶0;A̶1; button on your Xbox 360 controller. Provide the verification information required to recover your Gamertag.