It's fitting that we only learn the Wet Nurse's name at the moment of his death. In a lot of ways, he is the male Cherryl Brooks. As Hank Rearden's Washington advisor, the Wet Nurse is the victim of a terrible educational system and another tragic representative of the costs of that system and the strike:
He uttered nothing but uncertain opinions about physical nature – and nothing but categorical imperatives about men. (18.104.22.168)
Hank pities the Wet Nurse and is often angry on his behalf for the bad education he received. The Wet Nurse, like Cherryl, is basically doomed from the start; he was never given a chance to survive in the looters' world, and he dies in the effort to break free.
His other nickname from Hank is "Non-absolute," a reference to his type of education and value system. We see the Wet Nurse gradually start to question and then act against Washington. In the end he is killed in an effort to aid Hank, and at the moment of his tragic death we finally learn his name: Tony. Hank uses his first name almost as a blessing and a salute to the type of person the Wet Nurse gradually became. In a sense, he earned his name at the moment of his death by finally becoming an actual human being with good life values.