Good point! They ought to be able to locate the hypothesis that it really is two people in one, but with no understanding of the second person's importance, they might well just consider it "anomaly".

Considering who it is they're dealing with, I'd think that a more immediately available hypothesis is that Tom Riddle is another identity worn by the person who now calls himself Quirinus Quirrel. I certainly wouldn't discount the possibility that magic related to true names exists, and if so, anyone with an interest in concealing their identity in the long term is likely to have messed around with it.