Alright so I never actually read the book so please take this with a grain of salt. From what I have just read it seems that Gogol comes to accept his non-American side and appreciate his Indian-American identity. I'm not sure why he comes to terms with it, but apparently he does. In the ending he sits down and reads the book his dad gives him by Nikolai Gogol. So yes, I think he does accept his name. However I strongly encourage you to verify that if you have the book. I hope this helped :)
