Some of the themes in The Namesake are immigration into another country; assimilation into one's own lifestyle the customs, traditions and attitudes of the new country; marriage; home. Immigration into another country requires isolating yourself from family and friends and being a stranger in a unfamiliar country. Assimilation is difficult and is seen as a separate issue from the needs that inspire emigration. In The Namesake, Ashima held on to her culture, turning her back on assimilation by inviting other emigres to her home to celebrate traditional Bengali feasts and holidays.
Marriage is discussed in detail in the novel. Ashoke and Ashima had an arranged marriage that Ashima had little say about. Gogol lives with his wealthy American girlfriend until his father's death. Her parents had an openly affectionate marriage while his parents upheld the Bengal cultural dictate of not showing the private emotion of love in public settings. Gogol marries a Bengali friend at the advice of his parents but divorces a year later because his wife is restless and finds an alliance with another man.
The theme of home is connected to the one of marriage. Gogol doesn't where he feels at home. It's not in India where the family goes on holiday. He thinks it is with the American family until his father dies and he turns back to his mother and sister. Ashoke and Ashima always think of India as home. Lahiri evokes many of the shades of these complex themes in the story of Gogol (the name of a famous Russian writer chosen, because his work indirectly saved Ashoke's life), whose very name symbolizes ill-defined home and cultural allegiance.