Step 1. You will see the Guide button in the middle of the Xbox controller, just press it.
Step 2. Now, on the screen you will see your picture in the upper left corner, select the picture and press the A button on the controller.
Step 3. You need to select the My Profile option and then select the Customize option
Step 4 You will see the Gamertag option on the screen, select it and input the new Gamertag you want.
Step 5 If the Gamertag is not available the system will show it.
Step 6. At last, select the Claim it option and you will see that your Gamertag is now changed.
For More Details Click Here