The name has special meaning to Ashoke for various reasons. The first is because it is the last name of one of his favorite Russian authors. When he was 22 years old he was in a terrible train wreck in which he almost died. He was clutching a page of from "The Overcoat," a short story written by Nikolai Gogol. The only reason that the rescuers saw him was because he held up the hand that was holding the page and the page fell.
Another reason he feels a connection to the author Gogol is because both he and Nikolai Gogol spent most of their "adult life outside of [their] homeland". Ashoke tells his son this when he gives him the collected stories of Nikolai Gogol for his 14th birthday, which includes "The Overcoat."
He chose to name his son Gogol because his son represented the second miracle in his life, the first miracle being that he survived the accident.
The only real significance the name "Gogol" has in this book is that when faced with having to give his newborn son a name in order to take him home from the hospital, Ashoke Ganguli used the first name that popped into his head.
When he was younger and still living in India, Ashoke survived a train wreck. The only thing he was able to salvage from his belongings was a tattered copy of Gogol's novel "The Overcoat." For some reason, that name stuck in his memory, and that's what he named his son.