Your avatar's name is like your character's nickname in the game. 
If you want to give it a new name, here's how:

1. Go to Customization.

name_web1

2. Change Your Avatar's Name: Look for the option that lets you change your avatar's name.name_web2

3. Pick a New Name: Type in the new name you want your avatar to have.
4. Don't Forget to Save: Remember to click the 'Save' button to make sure your new name sticks.

The same goes for the mobile application.

name_mob1
 mob_name2  

That's it! With these steps, you can give your character a different name in the game and save it for good.