I believe this is meant to be paradoxical, not just mysterious. Let's take them in reverse order. In Chinese as in English, "name," 名 míng, also means "fame," or notoriety, as in "to make a name for oneself." Wise people are normally considered ones who have a reputation for wisdom. To say they don't is like saying 'smart people don't get good grades.' But Zhuangzi is full of paradigms who literally have no names but are known only by their titles, like "the butcher" in 3:02. And would-be sages who have attracted attention to themselves are criticized, like when he says of Lao Dan in 3:05 that he "did not want them to talk, but they talk. He did not want them to cry, but they cry." This is in keeping with the idea in the last note, 1:02 , that the goal is to disappear.
神 shén, "spirits," are usually juxtaposed to 鬼 guǐ, "ghosts," as mysterious entities responsible for otherwise inexplicable good fortune or harms. Prior to Zhuangzi the phrase 神人 shénrén, meant "spirits and people." He seems to have been the first one to coin the idea of "spiritual people." Graham translates shen as "daemonic," the power to make things happen without visible causes. In the human world this looks like magic but in the natural world it happens all the time, the way plants just grow. Thus the whole point of being a spiritual person is to effect change, so to say that a spiritual person accomplishes nothing is paradoxical, like a force that makes no difference.
If the interpretation of this line as deliberately paradoxical is correct, it may tell us something about what he means by 至人 zhìrén, "perfected people." 至 literally means "to arrive," so perhaps in this context it is a metaphor for "fulfilled" or "realized." If the perfected person has no self, what is there to perfect, fulfill, or realize?
Lest one were tempted, as I always am, so systematize this into a typology of three distinct ideals, Zhuangzi screws it up in 2.11 where he says "Perfect people are spiritual." So they are not three different goals but aspects of the same thing.