Lots of things have a narrator when one isn’t necessary, that’s not all that weird for a film and doesn’t tell the audience much.

nor are they defined as any third party in-universe like a detective making sense of it.

I don’t think that comparison works here. Most of the film is a flashback, described by the narrator. He doesn’t give his name as he tells us what led up to the prologue but that doesn’t seem all that odd, it doesn’t seem pertinent. Marla asks what his name is but the scene ends without us finding out - it’s relevant information to her but we have no particular reason to care whether his name is Dave Smith or Lance Elbowbottom III. It’s only later, with the reveal, that it becomes interesting. The credits might as well call him “also Tyler Durden” but “narrator” works well enough.