If you want to change your avatar, simply head to your profile page by tapping your avatar in the upper right hand corner. Once on your profile page, tap your avatar to choose a new one. Tap the 'Select' button once you've made your choice.
Step 1 - Tap your avatar on the upper right corner of the games page.
Step 2 - Tap your avatar on your profile page.
Step 3 - Scroll left and right to choose a new avatar.
Step 4 - Hit the 'Select' button.