I just thought they were trying to connect to the "youth" as Doctor Who had lost its cool and was "disconnected" with the teen audience, the BBC felt it had become a dinosaur from the past.
So, since all teenagers don't want to do what they are told, they invented a character they hope they could relate to - Ace. Ace was rebellious, she was a "teen" she didn't do what grown ups told her to do, you say your name is Doctor but I'm going to call you Professor, it was supposed to be affectionate but teenagers also like to tease. "My name is The Doctor", "yeah whatever Professor" ...