Yeah, as I understood it "The Professor" was more of a nick-name they gave him since he was so learned but not an actual title he earned (i.e. he wasn't an educator in a college or university) though he did hold degrees and doctorates.
I don't think the Professor's backstory was clearly enough developed to allow any certainty on that point. Certainly in Rescue from Gilligan's Island
he was treated as a full professor teaching at a university, although it's possible that could've been an honorary position resulting from his fame as a noted castaway/survivor.