It's just a nickname, as of course is "Ace". It presumably refers to his extensive knowledge. Ace used nicknames often, calling Mel Bush "Doughnut", for example. At the end of Dragonfire, the Doctor told Ace, "I'm the Doctor, not the Professor," but she continued to use "Professor". She also called him "Doctor". She seemed to use "Doctor" when a real name would be appropriate, such as when introducing him to others, and "Professor" when a nickname would be appropriate, in private or casual conversations.