You are not anonymous just because you are using a screen name. Pseudo-anonymous, maybe.
A lot of people in the chess world I know offline know this is my account (...)
Then you are not really (pseudo)anonymous, are you?
Some people know that I have a chess.com account but they don't know which one, so if I get banned for cheating and profanity and satanic rituals it will only affect "Irontiger" 's reputation.
You are not anonymous just because you are using a screen name. Pseudo-anonymous, maybe.
A lot of people in the chess world I know offline know this is my account even without me plastering my name all over it. If it was closed for cheating you bet your ass it would make me look bad to all those people.