*raises hand* David Tennant is right, his name is "The Doctor", but it's not wrong to call him "Doctor Who". Doctors One through Nine are called "DOCTOR WHO" in the credits! In fact, other former Doctors refer to him as "Doctor Who".
Did you know that in Doctor Who, the Doctor's bow tie is red if the episode takes place in the future, and blue if it is in the past? (It’s true for the tenth Doctor too. His suit was blue if they went forward in time and brown if backwards) MIND BLOWN