The first time you change your Casino World name, it is completely free. However, any time after that will cost 20 Gems.
When you change your name, all references to your old name will be replaced with the new one, so your friends will still be your friends, though they may no longer know who you are. Any gifts you have sent using your old name will now display your new name.
Here's some steps on how to change your name:
1. Click on Casino World in the upper left corner of the game.
2. Click on the gear icon in the upper right corner of the screen, then click on Settings.
3. When the Settings page opens, it should automatically be on Account Settings. The first setting will be Character Name and Icon.
4. Click Change Name next to your name. A new screen will pop up. Enter in your new name and click Change Name to save the change.