Answer:
Gogol's lack of choice by not choosing any of the provided options may be suggestive of the occupation he will take up later in life, i.e. architecture. It could also be suggestive of his inability to make up his mind on one thing, and constantly shifting from one point to another.
Step-by-step explanation:
Jhumpa Lahiri's The Namesake revolves around the story of how Gogol aka Nikhil Ganguli and his efforts to come to terms with his name. In his attempt to identify himself in the American land, he also comes to terms with the significance of his name and the story ends with him fully embracing his Indian identity and name.
According to Bengali culture, the "annaprasan" or rice ceremony is conducted to see what the future occupation the baby will become. But in this particular ceremony, Gogol did not choose any of the options given and would take up architecture. This may show that he will not become one of them, while also showing the vast opportunities available in America that is not known in India. This lack of choice may not necessarily mean that he will not become any of them, but also reveals the numerous other choices that are unknown to the Indian people. It could also mean his inability to decide on what he wants in his life, be it choosing his name, or having any relationship and even between his Indian heritage and his American upbringing.