I also love how Van Helsing isn’t this badass vampire hunter but just an adorable, eccentric little man who studies a lot about monsters. I pictured him as Guillermo Del Toro.
No, I think he's probably got the expertise to be a doctor, but much like it's hard to find a school that offers one in mad scientisting, a good vampire slaying graduate school is hard to find.
In one of the movie portrayals (Peter Cushing?) he presents a card listing a doctorate from Leiden. That had me considering which building they might have hidden that department in. Obviously one of the really old ones. Leiden bureaucracy is certainly Byzantine enough to hide whole fields.