What happens when I tap on my Profile Name?

Here, you will be presented with two options. You can choose either "Edit Name" or "Edit Avatar".

Choosing "Edit Name" allows you to rename your profile. Type in a new name by tapping on the text box, then tap the 25 Gold button to confirm. As stated in the following prompt, it may take a little while for some aspects of the game to update, and there will be a delay before you can change your name again.

Choosing "Edit Avatar" will bring up a screen where you can change your profile's avatar. This will appear to the left of your profile name and on PvP leaderboards. On the left, you will see two tabs, Avatar and Background. Avatar will allow you to change the face that is shown, and Background will allow you to change the background colour. To make a change, simply tap on the Avatar/Background you want, and then tap "Select" in the bottom-right corner to confirm the change.