while completely understandable, I will say that it's very easy to not miss anything, especially if you utilize the Wiki (which you absolutely should, along with the guide mod) and the vast vast majority of events are required.
as far as the Sensei thing goes, in context, it makes sense. it is a narrative point that Sensei does not remember his name, or more likely imo, is unable to for fear of a psychotic breakdown. I haven't finished the new update yet, but apparently his name does get revealed in some way in this update, although that is easily dozens and dozens of hours into the story. it should be noted though that for many of the girls, after developing your relationship with them, you can have them call you by most any name you'd like.