So dude, good for you who have fun immersing yourself in story. There are games that players can immerse themselves in, but many visual novels aren't necessarily meant for that, they're generally meant to be interactive books where the player chooses the character's fate.
But I didn't come to tell you how you should play, you play how you want. I just wanted to make my point.
However, I noticed that people only make this request to change the character's name when the game has a male protagonist, because when it's a game with a female protagonist, no one asks to add the ability to change her name and if they ask, it's a minority too small.
Anyway, if it's about immersion, instead of just asking them to add ability to choose the protagonist's name, why not ask to add ability to pick the protagonist's gender as well?
It is just a reflection here that I would like to leave for everyone.
Although I personally don't feel the need to add name choice or anything like that, as Ren is clearly a character, just note that the choices are displayed in third person.
Again, I just wanted to prove my point and not dictate how others should play, you are still free to play how you want and want to immerse yourself in the games.