Ed Norton plays the Narrator or Jack ( due to reading a book that described someone called Jack's body parts from a 1st person perspective). Meanwhile Brad Pitt is introduced as Tyler Durden. Later on we find out that they are the same person.
So is Tyler Durden the new name he has chosen which he went and made an ID for and got various part-time jobs under or is it his original name and he somehow keeps blanking it out when he needs to tell police (things like his apartment exploded, or that other things will explode) or when he sees it on his checks from work or his work documents Id and many other things that would have his name on them?