Answer: N. Scott Momaday - who is a native American himself - finds ironic that white people claimed that they were arriving into the "new world" when in reality there were ancient civilizations already living on those lands, and this claim is one that they have continued to sustain up to this day.
When Europeans arrived in 1492, there were very large Indian populations scattered all across America with a rich history and culture, an element that vastly defers the logic of the discovery of a "new world".
From the very beginning of the scene, as Benvolio is trying to get Mercutio to go home, Mercutio very clearly is trying to instigate a fight. When Tybalt approaches, all he does is sass him and turn his words around into jokes and puns. He says "And but one word with one of us? couple it with <span>something; make it a word and a blow," this taunting of Tybalt shows how badly he does want to fight. </span>
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 :)