Ashima and Ashoke's immigration has a profound impact on their son Gogol. He grows up surrounded by friends and peers who understand and move comfortably in American culture in a way his family life hasn't prepared him for. He feels like an outsider, especially because of his unconventional name; Gogol is neither American nor Bengalese. As he grows older he chooses to use his public name, Nikhil, and works hard to distance himself from his family in his quest to be American. He spends less time with his family, goes out with American girls, and anxiously (and angrily) awaits insensitive comments about his ethnic and cultural background. He becomes a part of Maxine's family until his father's death leads him to question his relationship to his family and his culture.
It's impossible to say that Gogol's difficult beginnings are entirely the result of his parents' decision to immigrate (no matter where you're from or where you've moved to, figuring out who you are is tough)—but their move to the US did change the course of his life and set him on a path full of questions and struggles with his identity and his relationship to his family.