You can find your username through your watch menu in-game.

Open your watch, navigate to your profile (top left on home menu)
 

You will find your display name and your username near the top of the profile tab.

Keep in mind that your username is not the same as your display name, all usernames are unique and while you can change your display name up to 3 times a week, you can only change your username once every 180 days. Your username will always start with "@".

If you're looking to change your @username instead, see this page for more info.