Gogol grows up resentful of his first name, which is neither Bengali nor American. To him, it represents how disconnected his Bengali family life is with his American life outside the home, and how he'll never quite fit in in the states (or in India, for that matter).
Gogol officially changes his name to Nikhil before heading to college. As Nikhil, he enters the adult world, gets a nice cushy job, and eventually falls in love and gets married.
Divorced after he finds out about his wife's affair, Gogol begins to make peace with the two sides of his identity, which we see when he begins to read the stories of his namesake, the Russian writer Gogol.