It can be argued that all three of the detective novels which make up The New York Trilogy have identity as a central theme.
In the first story, "City of Glass," we meet Daniel Quinn, who writes detective stores using the pen name William Wilson. Right away, we can see how identity will become a theme here, as by using a pseudonym, Quinn is hiding his true self from his readers. Later, Quinn decides to take on yet another identity—that of a detective named Paul Auster—and it is as Paul Auster that he experiences much of the action that takes place in this story.
The second story, "Ghosts," is quite confusing in terms of identity, because instead of having names, every character is called by the name of a color. When Blue is tasked with watching over Black, he soon gets bored because Black never goes anywhere or does anything. Blue therefore uses his imagination and starts making up stories in his mind about who Black is—and later about who Blue himself is as well.
Identity continues to play a significant role in our third story, called "The Locked Room." The identity of Sophie's missing husband, Fanshawe, haunts the writer's new life with Fanshawe's wife. The large volume of amazing novels, poems, and plays provide clues but no conclusive evidence about Fanshawe's personality and identity. Not knowing whether or not Fanshawe is still alive just about drives the writer crazy until he eventually gets the answers that he needs.