The Doctor isn't a name, it's a title, but is the Doctor really a Doctor and if so a Doctor of what?
In "The Armageddon Factor" the Time Lord Drax confirms that the Doctor actually does have a Doctorate.
Doctor of Medicine
Doctor of All Things
This article refers only to references within the classic series, not the new series.
The Time Crash blog was created to help New Who fans understand Classic Who references - and to know if something isn't a reference but a new idea. If there's a reference I missed or a subject that you feel needs more explaining, please comment.