it won't be impossible, but it is still very uncommon.
MC has a father to ask, and Neil should have given him some explanations in order not to answer him, if he had refused to answer him this would have created tension, curiosity about the matter, and it does not seem to be so
Neil may have lied to him, even in this case there must be a reason, and in any case if he had lied to him MC would still know his mother's surname, the fake one he was told, but he would be convinced that he knew.
it is very different not to know something, or to be convinced that you know it
and all this unlikely and dramatic situation would serve to make MC discover that he is a Burgmeister, who apart from exchanging Christmas greetings with Rusty, that would have additional consequences to the simple fact of belonging to a wealthy family (which he is already aware of) ?
The MC has seemingly asked Neil over the years, but his "memory" isn't so good and he never gives the MC a clear, straight answer, instead he goes off on tangents and mentions a lot of irrelevant details that ends up frustrating the MC. This much is made clear in ep 1 when we get a bit of the story of how the parents met and it's likely one of the reasons why the MC doesn't ask much about her.
Again, it doesn't seem the MC knows his mother's surname at all. In that story Neil tells, all the details are vague about who this "rich family" was and that's likely very much done on purpose. I see no reason why he absolutely has to have known what her surname was all this time because it's not exactly an important detail to know. He knows her first name and that's enough for him.
If the MC is revealed to be a Burgmeister, it opens up some very interesing angles, some of which can still work him gaining an inheritance and not the name of one of the college founders, but having that name would make these things even more impactful as it at least gives the sense of him having a higher standing than if he was just some random rich family legacy.
Only if you assume that Derek shoving a piece of cake into MC's mouth is part of MC's birthday celebration and not a do-over for the end of Hell Week. We know that some of the Diks feel bad about how Hell Week ended, it's far from inconceivable that they'd try to throw together a do-over.
The words "happy birthday" are literally in the tweet.
Apply Occam's razor and see if your hypothesis still works.
It may be fairly common for kids to grow up not knowing who their parents are but nothing we've been shown even hints at that scenario.
We know that he knows his mother's first name and that his Dad is an apparent terrible story teller when it comes to telling the tale of how he and Lynette got together and only ever says she came from a "rich family". Her family name isn't mentioned and that's likely deliberate on the part of DPC as it indicates that not only the MC doesn't know, but that it will be a consequential detail to be revealed later on.
You don't really believe this do you? I don't have the best relationship with my parents but I know they wouldn't let me attend a college founded by my great-grandparents without warning me that some of the students might be my cousins.
Yes, I do. A college campus is a big place and the MC comes from a completely lower social standing than the rich families of the college's founding fathers, so Neil probably doesn't think there's any chance he'd ever meet them since they would typically run in different circles. But, plot contrivances being what they are, he has interacted with them when most people in the MC's position aren't normally likely to hang out with the rich legacy kids. It's like if someone like him attended the same college as a member of the Walton family; in the real-world, there's very little chance they'd ever meet due to their different social standings.
The thing always has been for me that, if Neil is indeed keeping such a secret from the MC, even when faced with him attending B&R and the small likelihood of running into distant relatives, then he must have a damn good (or at least justifiable) reason for not telling him and also for hoping that the secret can be kept despite these things.