As someone who likes to self-insert while playing these games, I do prefer it if the game has the option for the player to name the MC. However, I have played games where self-inserting just isn't possible because of, for example, the way the MC is, even if you can name him whatever you like. It's not like I name the MC after my real name, though, so it's not that bad. It's just that I usually begin playing a game with the mindset that I'm going to become that MC while I'm in that particular virtual world setting, so when he turns out to be a prick then I'd have to deliberately force-quit the start of a mental/emotional connection and then start perceiving the game from the less intimate, third-person perspective instead. That, to me, is the process that can get a bit annoying when that happens. Doesn't happen that often, though, because I try to choose games that have at least moderately likeable MCs (however I do NOT have 100% success rate, LOL).
At the end of the day, I think it really depends on what kind of experience a player wants out of the game. If a player wants to become the MC for the duration of the playthrough, then I feel like it makes more sense to have the option to name the MC. It is an alluring thought because you get to experience romantic instances with various LIs, and if you can find them attractive then the idea of you being the MC becomes that much more appealing which, in turn, may put more importance onto having the option to name the MC whatever you like because, that way, the game feels like it's been personalized to your liking that much more. (Holy shit, that was one messy sentence if there ever was one! lmao)
That is, of course, if you can find the MC likeable in the first place. If not, then all bets are off. The MC could be called Mr. Dingbat for all I care, and I wouldn't be losing sleep over that even if I couldn't change it, if I can't feel comfortable self-inserting as the guy in question.