It's established sometime in the Fourth Doctor's time that his name is something like Ips, in contrast with the standard Gallifreyan long names like Romanadevoratrelunder (which is how it's pronounced, even if I blew the spelling). "The Doctor" is a title that became a name, and I think it's more akin to Professor than to Healer.

And Brigadier Lefbridge-Stewart is the cold rock stuff. You'll love him. All over the Third and early Fourth doctor.