Doctor Who logo (in-universe)

The Fifth Doctor recalled that his book series was to be named with a comma, The Doctor, Who Discovers but became Doctor Who Discovers after "some idiot" in the publisher's design department missed the "The", creating a logo that said Doctor Who. (AUDIO: The Kingmaker) According to other accounts, Doctor Who was the name of a a dramatised documentary series about the Doctor which had been broadcast on television as early as 1963. (PROSE: Dalek Survival Guide, TV: Remembrance of the Daleks)

In the mid-2000s, a new logo featured on billboard advertisements for the Doctor Who Exhibition which were placed around Cardiff. (TV: Everything Changes)

Parallel universes
In a parallel universe visited by the Eleventh Doctor, Doctor Who was a fictional television series and had varying logos, with a different logo appearing on the DVD release of The Twin Dilemma and Doctor Who The Official Annual 2007. (COMIC: The Girl Who Loved Doctor Who)