If you want to change your current name, all you have to do is:
  1. Tap your name on the top left corner of the home screen
  2. This will open your profile; from there, tap the "pencil" icon beside your name
  3. A pop-up will appear where you'll be able to type in your new name and confirm it.
You’ll be able to pick your username after completing the tutorial. The first time you change your name after the tutorial, it will be free. The second time, it will cost you 50 Diamonds to do so.

Keep in mind that your username must contain from 3 to 12 characters, and they must never have any abusive content. Otherwise, your account might be banned from the game.