Professor

Professor was a title given and used by a variety of people throughout history, usually (though not limited to) peoples of university educated pedigree.

Ace referred to the Doctor as Professor throughout her early association with him (DW: Dragonfire et al) and often continued to refer to him as 'Professor' in a friendly manner several years later. (NA: Happy Endings) Allthough somtimes this irritated the doctor he grew used to it

In the year 100,000,000,000,000, Yana was given the title of professor, despite there being no universities for over a century. (DW: Utopia)

Specific professorships
Bernice Summerfield originally faked her qualifications as a professor of archaeology; however she did eventually obtain a professorship. (NA: Love and War, Return of the Living Dad)

River Song introduced herself as a professor at a university of archaeology. (DW: Silence in the Library)