Changing your name is easy. Simply select your profile picture which appears at the top right corner of the main menu screen. Tap the name button to change your name, and after you choose your name and press ‘Okay’, your new name will be set.
Or, tap on the golfer profile icon displayed in the middle of the main lobby screen. Tap the small pencil icon to edit your name from there.

Pick your name carefully; it costs 300 Gems every time you change it.