How can I recover my gamertag?
Solution 1:
Gamertags are not stored on the console, so it should still be available.
To be sure you can try logging into the xbox website. There is many ways to recover your gamertag if you forgot the login information as well.
Solution 2:
Press the Xbox button once the console is on and connected to an active internet connection. Choose 'recover gamertag'. Then enter your email relating to the gamertag. You will then be promted to enter the password for that email. The profile will be downloaded to the storage of your device chosen. You won't have your save games, however your achievements as of the last time you were online will still be there.