There is absolutely symbolism in this, and in fact the title of this excellent work is linked to the way that the narrator remains anonymous throughout the entire text. One of the key themes of the novel is the way that the narrator is shown to be engaged on a search for his own identity, and yet he quickly learns that being black makes him invisible to white eyes as they variously abuse or ignore him. What is ironic about this search for self-identity is the way that others are able to recognise the narrator's invisbility well before he himself is able to recognise and accept it. Note what the vet at the Golden Day says to Mr. Norton concerning the narrator:
Already he is—well, bless my soul! Behold! A walking zombie! Already he's learned to repress not only his emotions but his humanity. He's invisible, a walking personification of the Negative, the most perfect achievement of your dreams, sir! The mechanical man!
Of course, remaining anonymous emphasises the hero's invisibility, as not having a name helps create and support the sense in which the hero does not actually have an identity that is accepted in white dominated society. To support this idea, note the way that Mr. Bledsoe says to the narrator, "You're nobody, son. You don't exist—can't you see that?" At every turn, the narrator is forced to realise that the colour of his skin makes him invisible, somebody that does not count, and his anonymity only reinforces this impression.