Do you realize that if that option never became a "thing," your life would go along just fine?
How about this? Play the game as it is, and then decide if you didn't become immersed in it.
But you have to give it an unbiased chance, as Twisted Rabbit said. ( well-crafted dialogues and a rich game world have a far greater impact on immersion than a simple name change!)
So many here ask for a game curated to their tastes before even playing. You are limiting your experiences in life if you already know what to expect.
Incoming Faceplams from the millennials.
Did you not become immersed in The Hobbit? And Millions of other fictional stories?