The character played by Mr. Norton is called 'The Narrator' in the end credits. Much effort is spent to avoid him giving his name. He is not 'Jack' because he found out that verbal trick quite late, and how then could he be Jack's Raging Bile Duct?. He is not 'Tyler', because - nuts or not - he would not read out the name he had just used at check-in as if he had never heard it before. He has a perfectly normal waking name that is deliberately kept hidden to increase his anonymity. It could be your name.
On the other hand, as Alex said, his 'real' name could be Jack. There's no reason not to. but it certainly isn't anything as ridiculously cool as 'Tyler Durden'. he wouldn't have grown up like that if it was...