Instructions
Disconnect the hard drive of the old Xbox 360 console, if you have not already.
Connect the transfer cable to the old Xbox 360 hard drive. Plug the USB end of the transfer cable into a USB on the new Xbox 360 console (with the power off).
Power on the new Xbox 360 console. Select "Yes, transfer to console" from the dialog that appears when the hard drive is detected.
Select "Start" to begin transferring the data from your old Xbox to the new one. It may take several hours to complete.
Navigate to "My Xbox" to log in to your Xbox Live account when the transfer completes.
Select your gamertag within the "My Xbox" menu, select "Change Gamertag."
Select "Enter New Gamertag." Enter your new, modified gamertag. Click "Yes, use this gamertag" to save the changes.