Max is nicknamed Whisper because there's something wrong with his throat so he can only speak in a whisper. He owns a gambling joint, but we aren't given much back story on him beyond that.
Out of all the gangsters, Max gets the most screen time. The Op interacts with Max quite a bit, but just as we start thinking they're becoming good pals, we realize that the Op is merely using Max as a pawn to pit the other gangsters against each other. That's harsh, Mr. Op.
Part of the difficulty of reading Red Harvest is the fact that the gangsters all seem to be pretty similar. We don't know their personal backgrounds so it's hard to keep them straight, and their motives are rarely explained in a clear way.
With regard to Max, he's constantly on the run and hiding from the police, but when he decides to kill Dan, we're not given any explanation as to why or how that came about. The effect of not being able to witness half of the murders that take place creates a pervasive atmosphere of death in which we're waiting for the next character to drop dead.
It doesn't even come as a surprise to us when Max is shot and killed (again offstage). And Hammett doesn't even give us any space to let these deaths sink in before moving onto the next dead body. So five minutes after Whisper is killed, we witness the death scene of Reno. We can't help feeling that all these murders are slightly pointless.