I'm not offended, I have simply never heard anyone claim that being able to change your name in a video game "completely ruins immersive aspects" before. Please elaborate as to why you think this.
Oh, I see! Sorry, I gotcha. I'm not a native speaker, so pardon me in case my answer isn't worded perfectly.
Well, I wasn't speaking about "my immersion" as such. I was more trying to describe Nintendo's idea of wanting players to create a world. The names are the fundament of your save file (insert talk about the meaning of variables in programming) and anything you're going to do in the future. That's where it all begins.
It's true that you can change your name in real life, but (from what I know, I never took a deeper look into this topic) you can't do it whenever you feel like it, as if you were making a cup of coffee. You have to submit an application, you have to wait, you have to pay money for it (at least where I live) and you can't do it as often as you like. I guess in the end it comes down to the value that names have in our society. What's the first thing you exchange with a stranger whom you want to get to know better? It'll probably be the name and/or where you come from.
Being able to change the character's or the place's name whenever you want would change the way a lot of people look at their game, likely to affect their attachment to it (which is part of the whole Animal Crossing experience), making the world feel less personal and unique. The names would become "yet another option" you can customize at any time, turning even the last bit of the game into something arbitrary.
While that may be nice for people who later regret their choices or who just like to mess around in general, it'd take away this element of a consistent world that you're being thrown into. Sure, cities/towns/islands may have changed their names, but I'm quite sure people had a lot of different opinions about that as well and just imagine the name of the place you live in changing randomly all the time...
If we're talking about an option to change it once (maybe I should've asked about that first lol) or just once within a certain period of time, it'd be different because that'd mean you still have to put some effort into whatever you come up with. I wouldn't say anything against that.
Edit: I may have gotten a bit carried away here... Basically, tl;dr: Names and their role in identification and emotional attachment.