So what does he want to be called? Just a rat? But - there are actual rats, which are already called rats. Unless those don't exist in this universe, "ratman" seems like a pretty reasonable term. He has both rat and humanoid features.
Yeah. Him calling the man "man-rat" makes no sense though. For it to make sense, there would have to be something even more human and more distant from rats, so that he could be viewed as half rat.
But the human calls the rat-person a ratman because they seem to be something between a human and a rat. The human would call a regular rat a rat. Why would the rat-person call the human a man-rat, if the human is a regular human? Who would he call man then?