Not to rain on your shit-on-Fuckface parade, but that last reply makes it seem like he knew she was a Morgan just not a Morgan-Burke
That's the way it reads to me too.
I really seem to be the only one who is okay with this. Sure, it would be nice if we knew the characters' last names, but just because we don't know them doesn't mean that MC doesn't. It would be nice if Sage actually introduced herself as Morgan in the earlier episodes. Or it were revealed some other way. It wouldn't be that hard. Just have teacher call her "Ms. Morgan-" and have Sage cut them off with "I prefer Sage" before they add "Burke". It's a bit sloppy that it doesn't happen, but hardly game breaking.
Still there are three points that make this completely believable.
1. It's typical for college students to introduce themselves with only their first names, especially in relaxed situation's like parties.
2. MC has been at college for about two months at that point. Eventually he will no doubt hear people's last names, but the keyword is eventually. Two months is not too long for a name to stay secret when the person in question takes pains to make it so.
3. There is no situation where MC would be guaranteed to hear that Sage is a Burke. They are not in the same classes where a teacher would say it. All her friends just call her Sage and respect her wish to distance herself from the Burkes. She quite normally refers to her family as "mom", "dad" and "brother".
Honestly, Jade insisting that everyone should know them because they are the "elites of B&R" is much weirder than a freshman not knowing them. Yeah, "elites" of a small college. In that MC is completely normal and Jade is just full of herself.
He does not even know that Jill is a Royce while most people on the campus knows who she is
Again he has been there for two weeks when he finds that out. Seriously these people are weirdly full of their very local fame. And you are all really weird for buying into it.