When your Arcanox castle is connected to Google+ and you start the game, you might see this prompt since a few days, weeks or months:
Google has introduced the Gamer ID to detach the Google+ profile from Google Play, because many people don’t like to see all their Google+ friends the games they play. This means more privacy for you.
That’s why I recommend to pick a name and click on “Sign In”. You have to create the Gamer ID only once and not for every single game.
You can read all details about the Gamer ID here.