How is this done?
 

How is it possible to make one person be two or three different characters, depending on a forum.

Say a person registers as Jane Doe. That is her main board username, and that is what she goes by. However, when she enters into certain forums, say an RPG forum, when she posts, it no longer shows her posting as Jane Doe, it shows her posting as Dora Explorer.

How is this done?

Could be done any number of ways... perhaps Dora Explorer is a user profile field and so when you enter that other forum, it uses FieldX for the username.

Is there a specific hack that has this done already or a how to somewhere?

I haven't seen a modification released, but I do remember helping someone with parts of their version of this modification in a thread a while ago. I don't remember how much of his code he posted in the thread though.

Basically, just use a new style for the other forum and go into the postbit(_legacy) template and replace $post[musername] with $post[fieldx].