If you want to change your name in the game, you must connect your game to Facebook. After you do so, your photo and name will automatically appear in the game instead of a blank icon.
How do I do it? Go to Settings, then Accounts, press the "Login with Facebook" button, and follow the instructions. This will also help you keep your game progress safe. Please note that, after you complete the above steps, your Facebook profile icon will appear in the game's settings.