I agree that assassin should be changed to something else. I think that they would have a problem if they ever wanted add a proper assassin character in...I personaly like Champion.
again, please understand that the word assassin does not mean "ninja", "sneaky", "rogue", or "covert". It means a person who commits murder, especially one who murders a politically important person either for hire or from fanatical motives. Thats it. There is no requirement that an assassin be covert its just that to accomplish a murder of a politically important person these days, you have to be covert, or sneaky, or ninja-like to penetrate the security that has been set up to protect said person.
However, on the battlefield, particularly with DemiGod, it means your focus is to kill/murder important persons on the field (opposing players). There is no particular security to bypass other than the armed masses so the need to be covert (see Rook) can be negated. So yeah, assassin sort of works. It may not be the best descriptor (perhaps champion is better), but it does distinguish that player from a general-type well.