So, this is a catchy title. That's probably the first thing you notice about it. The second thing you might notice about the title is that Hosseini didn't name the book The Kite FIGHTER. Which means Hosseini didn't title his novel, weirdly enough, after his main character. (Even though Amir narrates pretty much the whole novel and is the protagonist.) Why would Hosseini put Hassan – a Kite RUNNER – at the center of the novel? One answer might be that Hassan haunts Amir and is, in one way or another, the subject of Amir's thoughts for pretty much his whole life.
It's also worth mentioning that at the end of the novel, Amir does become a kite runner. The book ends with Amir running a kite for Sohrab. It seems to be another step on his path to redemption that he does for Hassan's son what Hassan used to do for him.
We also need to point out that the title insists on the symbolic and narrative importance of kite fighting. Why is kite fighting so important? Isn't it just a game Amir and Hassan play? We're glad you asked. Kite fighting precedes the horrific rape scene in the novel. It's a symbol of both innocence and the loss of innocence. You can also see it as a symbol of redemption (see "Symbols, Imagery, Allegory: Kite Fighting" for more).