In his relationships with both Maxine and Moushoumi, Gogol adopts his partner's identity (or what he perceives that identity to be) because he has not yet solidified and accepted his own identity.
When he is with Maxine, Gogol fully integrates himself into Maxine's family—living with her parents, dining the way they dine, befriending the types of people they befriend, and reading what they read. He misses holidays with his own family to spend them with Maxine's family, celebrating according to their traditions instead of his own. Maxine's remarkable security in her identity overpowers Gogol's own tenuous sense of himself. It is only after his father dies that Gogol's connection to his family and his heritage are strengthened. At this point, after realizing that he cannot live without his family and his ties to the Indian-American culture he grew up with, he rejects the false self he has created to be with Maxine, which ends their relationship.
When Gogol is with Moushoumi, he feels a deep sense of relief to be with another second-generation Indian-American with an upbringing similar to his own. He is so focused on the comfort of their superficial similarities and so desperate for a connection to his culture that he ignores the fundamental differences in their characters and their deepest desires. He throws himself into the parts of their relationship that involve their families and shared background, like their traditional wedding and their holiday celebrations, and fails to realize that Moushoumi is distancing herself from him. After her affair, when he accepts that their marriage is over, Gogol returns to his family. It is only here that he is able to fully become himself, stepping back into his role in the family and accepting the gift of his name given to him by his father.