Of course the media outlet can ban anybody for any reason because the first >amendment only applies to the government restricting free speech.
Unless it is done to commit some kind of crime like fraud or identity theft, it's hard to see how merely posting under another name would be illegal.
It would be similar to meeting someone at a party and introducing yourself
as B when your name is A. Unless you're trying to commit some kind of identity-related crime, I think you can legally do that.
Of course the media outlet can ban anybody for any reason because the first amendment only applies to the government restricting free speech.
If person B is a real person that you are impersonating and then you
attempt fraud or defamation of them then you could be canceled by the
host. You could also be criminally prosecuted for fraudulent actions.
You could be civilly sued for defamation in many countries.
No, I'm not the famous dead Bank Robber John Dillinger. But no one
actually believes I am either.