I assume you are referring to the novel The Namesake by Jhumpa Lahiri. Ashoke and Mrs. Lapidus are two characters who contribute to the development of the plot by creating a conflict over Gogol's name and identity.
Ashoke is Gogol's father, a Bengali immigrant who has a strong attachment to the Russian writer Nikolai Gogol, whose book saved his life in a train accident. He gives his son the pet name Gogol, intending it to be a temporary name until his grandmother sends them a formal name from India. However, the letter never arrives, and Gogol becomes the official name of his son.
Mrs. Lapidus is the principal of Gogol's kindergarten. She is an American woman who respects the wishes of the children over their parents. When Ashoke introduces Gogol as Nikhil, his chosen good name, Mrs. Lapidus asks Gogol what he prefers to be called. Gogol says Gogol, and Mrs. Lapidus registers him as such.
The conflict between Ashoke and Mrs. Lapidus reveals the external clash between Ashoke's traditional Indian culture and American culture, as well as the internal struggle within Gogol over his name and identity. Ashoke wants his son to have a proper Bengali name that reflects his heritage and culture, while Mrs. Lapidus wants him to have a name that he likes and feels comfortable with. Gogol is caught between these two forces, and he grows up feeling confused and unhappy about his name, which he later tries to change.
The conflict also foreshadows the main theme of the novel, which is the search for identity and belonging in a multicultural society. Gogol's name becomes a symbol of his hybrid identity, which he has to navigate throughout his life. He has to deal with the expectations of his parents, who want him to follow their traditions and values, and the influences of his American peers, who expose him to different lifestyles and choices. He has to find a balance between his two cultures, and a sense of who he really is.
I hope this helps you understand how Ashoke and Mrs. Lapidus contribute to the development of the plot in The Namesake. If you have any more questions, feel free to ask me