Why is the narrator's real name or brotherhood name never revealed in Invisible Man? Is there symbolism behind this?

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:

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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.