Last month, Google announced that new Play Games users would get a player ID instead of having to make a Google+ account. Player IDs are now being rebranded as Gamer ID and will act as an in-game identity. As they are unique, Google recommends heading to the Play Games app now to claim yours.
Gamer IDs will be used to represent users instead of their actual identity like with the previous Google+ system. Gamers will be able to select a unique handle, but must choose from one of over 40 pre-made avatars by Google. During setup, users will also have the option to make their game activity public or private and the ability to associate their Gamer ID with their actual name and email address.
As Gamer IDs are unique, Google recommends users claim their handles now in the Play Games app. Otherwise, new users will be prompted to set up an ID the first time they use an app with Play Games integration. As previously announced, users will now automatically be signed into games after their initial log-in. Presumably, users who already have an account based on their Google+ profile will be able to switch over to Gamer IDs.
These changes will likely require an updated version of Play Games to take effect.