If you're playing connected to a King account, then simply follow these steps:

Your profile settings can be accessed by tapping on "My account"/"Profile" /"My Profile", depending on the game.
To change your name or email address:
1.- Type in your current password

2.- Change your email or first/last name and tab on submit

To change your profile picture:
1.- Tap on the camera icon

2.- Tap on the "Plus" sign or on Add Picture

"I can't find the camera icon in my game"
We’re currently working on the player profile feature, and as a consequence, some players don't have the option to change their profile picture at the moment. There's nothing wrong with your account or device, so don't worry, and please accept our apologies for the inconveniences.
Facebook account
If you are connected to the game via Facebook, your Facebook profile name and picture will show in the game. Simply log into your own Facebook account please, and make the changes there.
Please note that the changes may take a few hours to be published into your game profile.