Why did Paul Auster introduce the character named Paul Auster in his novel City of Glass?
This is a question of sheer speculation unless you can get in touch with the author and ask ask him yourself!
City of Glass, the first book of an urban trilogy, introduced the side character Paul Auster only indirectly since the protagonist gets involved with a case as the result of a mistaken phone call (in which the caller is seeking the services of a certain Paul Auster, detective) and ends up speaking to someone else instead. The investigator in question only shows up much later on in the story, and even then in only a very unobstrusive way. Perhaps the nonsense side of life, where the fate of one depends only the conjuncture of a couple of haphazard events, interplays here. At any rate, this is one theme fully exploited in Auster's "Smoke" and in a shorter work "Lulu on the Bridge."
The personnage of 'Paul Auster' appears only in the background of this story incognito, much as Hitchcock's phantom appearances (of himself in person) in most of his films as some obscure person in the background. You catch just a flash glance of him, but when you look again, he is gone.
Check out the following site for more information:
Another critic wrote a book review of City of Glass in which your question became a kind of personal obsession. You can see what he has to say by clicking on the first reference below.