Quote 4
In history class, Gogol has learned that European immigrants had their names changed at Ellis Island, that slaves renamed themselves once they were emancipated. Though Gogol doesn't know it, even Nikolai Gogol renamed himself, simplifying his surname at the age of twenty-two from Gogol-Yanovsky to Gogol upon publication in the Literary Gazette. (5.1)
It turns out name changing has been a rite of passage for many immigrants to the United States. Maybe this is what makes Gogol so willing to change his name to Nikhil. Even though that name is Indian, and therefore foreign, it's still a way for him to participate in the immigrant experience.
Quote 5
"There's no such thing as a perfect name. I think that human beings should be allowed to name themselves when they turn eighteen," he adds. "Until then, pronouns." (10.113)
Gogol's attitude toward names is even more radical than his parents, who stick with the Bengali custom of pet names until they decide on a formal name. He seems to think that you can't know who you are until you're at least eighteen, so why have a name before then? This implies, of course, that a name has something to do with who you are. Do you put as much stock in names as Gogol does?
Quote 6
Without people in the world to call him Gogol, no matter how long he himself lives, Gogol Ganguli will, once and for all, vanish from the lips of loved ones, and so, cease to exist. Yet the thought of this eventual demise provides no sense of victory, no solace. It provides no solace at all. (12.24)
Gogol's identity is closely tied to his name. By the end of the novel, the idea that there might be a time where no family members will be around to call him "Gogol" saddens him. Maybe he likes that name a bit more than he realized, not because of how it sounds, but because of who calls him that.