The first reference to the Reader's Digest magazines, and the articles from which this device originates, is in chapter 7 of the book.
In the oldest magazines, there's a series of articles where organs in the human body talk about themselves in the first person: I am Jane's Uterus.
I am Joe's Prostate.
No kidding, and Tyler comes to the kitchen table with his hickies and no shirt and says, blah, blah, blah, blah, he met Marla Singer last night and they had sex.
Hearing this, I am totally Joe's Gallbladder.
Fight Club,
Chuck Palahniuk - Chapter 7
In the book it was Joe, for the film this was changed to Jack. Likewise, Jane was changed to Jill.
Because of Edward Norton's character in the film frequently using these phrases to express his feelings ("I am Jack's Complete Lack of Surprise"), some people (including the crew on the film set) call this character Jack.
I really can't see why, other than for the convenience of having something to call him.
"The Narrator " is what I tend to call him, because that's what he's listed as in the movie credits, and in the book he takes the narrative first person perspective. This, sadly, seems to have become quite popular, to the extent that on the DVD he is (apparently) called Jack. I have also heard that in certain scenes of the DVD he is captioned as "Rupert" (this being just one of the many fake names he gives at the self-help meetings.
In actual fact, we never learn the narrator's name. In the film, one scene ends with the Narrator giving Marla his phone number, and her saying that he forgot to put his name. A bus goes past. The scene ends.
In short, I am Joe's ... (or Jack's ...) is NOT a hidden clue as to the Narrator's name. Any search for this name is futile (there is a rather irritating discussion on IMDB which illustrates this quite nicely. "It's Jack", "It's Joe", "isn't it Rupert?"). It's a very funny narrative device.