In order to change your name and photo in the game you need to connect the game to Facebook, go to the Settings of the game , and click the "Connect" button and follow the further instructions. This will also help keep your game progress safe.
Please note that your Facebook profile icon will appear in the game settings afterward as shown on a screenshot:
If you are not willing to show your avatar, you may try to change it by tapping on a pencil icon and choose from the proposed avatars.
The same applies to the procedure of changing your name. Tap on a pencil icon near your name and change it.