Considering the importance of The Overcoat by Nikolai Gogol to the writing of The Namesake by Juhmpa Lahiri, I believe it is possible to draw a line connecting the main characters of both books, and their overcoats.
For Gogol (The Namesake), his overcoat is not literally an overcoat, but his changed name, Nikhil. An overcoat is used to cover, in this sense Gogol is covering up the truth of his real name because he is too embarrassed by it.
In The Overcoat by Nikolai Gogol, Akaky (the main character) acquires a new overcoat, and with it becomes someone new. He pretends to be someone he is not until that overcoat is lost and he returns to his original status.
(Go to 3:30 if you want to see Akaky and his overcoat)
Similarily, despite the acquisition of his overcoat, Gogol (The Namesake) still remains Gogol to his parents. When his father dies, he returns home and sheds his overcoat, becoming Gogol, rather than Nikhil, once again.
Personally I believe in both cases the the overcoat represents the defiance of fate. It represents the will to go past what has been predetermined for you. However, it appears that fate, in the end, is inescapable in both cases.