Hmm. If it was like that from the start, I'd defend it from an artistic standpoint and say that it's honestly pretty ridiculous that people just expect a customizable protagonist name to be the standard in literally every game (except games with female protagonists, which demonstrates the double standard). However, I can see it being an issue that the option simply got removed in an update after having already been there for a while.
That being said, I do recall some moments in the dialogue that wouldn't work well with a custom name, and are likely to crop up somewhat often in a game about hypnosis. Namely when a hypnotized character would mutter part of Alex's name, which got confusing if your name wasn't Alex. If you named your character Dookienuts, it'd be pretty tough to set the game up to dynamically have a character say, "I love... D... Doo... kie..." (Edit: And wouldn't you know it, a line like that shows up in this latest update.)
...I'm still seeing my custom name show up as the speaker when using my old save, though. I guess that's an oversight. I noticed that after noticing that one of the lines in Helen's hypnosis is missing the name despite not being narration. (Specifically, the "breathing increases your pleasure" part.)
One last issue to report: In the replay menu, when choosing the MC option (who should probably just be called Alex here as well if it's not gonna be custom anymore), the full list of scenes trails off the top of the screen. Since you can't scroll, this should be separated into two pages.