I think that one major element of Gogol's characterization is confusion. Gogol is confused about much related to his identity and his sense of being in the world. It is almost to the point where he consistently does not recognize who he is and what he thinks turns out to be something that evolves into something else. Gogol thinks that his identity is "American" and has no trace of Bengali roots. At the same time, his identity is one that is divergent from his parents. However, with his father's death and the moment of reckoning within him that a loss has been experienced, Gogol moves closer to his family and closer to his Bengal identity. This culminates with him going to India to marry Moushimi, a relationship that reveals more questions about him and his own beliefs than anything else. In the end, when this relationship fails, Gogol has to endure more questioning. This allows him to better understand who he is and allows him to embrace his father's naming him, something that represents him starting the process of moving closer to personal comfort and a more stable sense of identity when all else is gone from him. It is here where Gogol's character finally emerges out of the shadows of uncertainty and takes a step towards solid ground in defining who he is and upon what values he is to place primacy.
Much of Gogol’s character can be understood in relation to a clever bit of foreshadowing that takes place when Gogol is six months old. During the Rice Ceremony, Gogol must choose between a dollar, a pen, and earth, each of which represents an adult profession; instead, he chooses none and cries. Unlike his six-month-old self, an adult Gogol chooses to firmly embrace American culture and rebel against his Bengalese heritage as an adolescent and young adult. He finds lengthy trips to India uncomfortable—as does his sister Sonia—and prefers to assimilate into America to a degree that his parents never did. He goes so far as to change his name, which he feels has burdened him for his entire life, and adopts a name that can be shortened to sound American. For part of the story, at least, Gogol’s choice is clear: in a battle between American culture and Bengalese culture, American culture is the resounding winner.
Gogol finds ambiguity difficult. As a result, he appears harsh in his efforts to distance himself from his parents and their shared culture. In truth, this actually showcases his own insecurity. He rejects his birth name for ludicrous reasons (arguing he couldn’t ask a girl out if his name was Gogol) and attributes his later success in relationships to his changed name, seemingly unaware that the problem had little to do with his name. To his mind, his problems are always due to external factors: his Bengalese heritage, his non-assimilating parents and extended family in India, his Russian name. In light of this, it makes sense that Gogol throws himself so fully into American culture. It is possible that Gogol believes his problems will disappear if he can assimilate fully.
Nonetheless, Gogol finds himself adrift after his father’s death. The revelation of his namesake has brought him closer to his family; following his father’s death he withdraws from his American girlfriend and becomes ensconced in his own family. When she becomes engaged to another man, he is largely unperturbed. Gogol is inflexible and largely incapable of holding two seemingly contradictory ideas at the same time. His acceptance of Bengalese culture runs parallel to his rejection of American culture. When he accepts his mother’s advice and asks Moushumi, a Bengalese woman, to marry him, his transformation is complete.
Gogol’s rigid nature is content for a time because he chose a side. This does not last, though: Moushumi has an affair with a man, so his marriage ends. After rejecting American culture and having been failed by Bengalese culture, Gogol turns back to his namesake. In many ways, the story ends where it began: with Gogol surrounded by various manifestations of his identity, possessing all and yet none. It is ironic that, unlike his infant self, it is not for lack of effort that Gogol finds himself in such a position—while Gogol is rarely likable, his efforts to establish an identity are sincere. He has embraced and rejected two cultures; now, at last, Gogol appears ready to define himself by his own terms.