You should start using your emails when you log on.

The other players will NOT see your email address, so there is nothing for you to worry about.
The change is done to prevent various players from creating multiple accounts.
Also, it should make it easier for the new players. It means that if you have an email address, you will know how to log on to the game.
If you do not have an email address, then probably you should not be playing online games.