When a “true fan” of Doctor Who wants to get really pedantic, they’ll correct a casual viewer who accidentally calls the title character Doctor Who rather than just the Doctor.
“Well, actually…his name is just the Doctor.”
And that’s kind of true. Usually in the show, the mysterious Time Lord is simply known as the Doctor. But sometimes they go by Doctor Who, as well. And no, I’m not talking about the Peter Cushing version…or the fact that the end credits of every episode for 26 years credited the main character as “Doctor Who.”
Here’s a few examples of when the Doctor added the “Who” surname.
The Gunfighters
In “The Celestial Toymaker,” the Doctor outwitted the nefarious Toymaker, but the reality warper got his vengeance through a piece of candy.
Although the end of that series makes it seem like the Doctor might be poisoned or worse, in reality he just hurts his tooth on the hard candy. At this time, the Doctor couldn’t control where the TARDIS landed, so he had to seek out a dentist at the first place he found: the American old west.
“The Gunfighters” is a comical little serial with a remarkably high body count at the end. It also introduces the first time the Doctor calls himself “Doctor Who,” albeit in an indirect fashion.
The Doctor: Allow me, sir, to introduce Miss Dodo Dupont, wizard of the ivory keys, and er Steven Regret, tenor. And lastly sir, your humble servant Doctor Caligari.
Masterson: Doctor who?
The Doctor: Yes, quite right.
This was the First Doctor in his impish old man phase, so you can tell that he’s having some fun despite his aching tooth.
The War Machines
Two stories later, the Doctor finds himself back on Earth in the 1960s and facing a superintelligent computer, WOTAN.

Naturally, WOTAN is up to no good. It brainwashes scientists and even the Doctor’s own companion Dodo. It does all this with the intention of recruiting the one “human” brain that can help it fulfill its goals of global domination. When WOTAN demands the Doctor, it says:
“Doctor Who is required! Bring him here!”
And just like that, he’s Doctor Who for the rest of the serial. Multiple people refer to him as Doctor Who for the rest of the story. Although the Doctor himself never uses the name, it’s like everyone involved in the story forgot that Doctor Who was supposed to be the title of the show, not the name of the character.
The Highlanders
“The Highlanders” is probably one of the most significant missing serials, and one of the top ones that I wish the BBC would either find or reconstruct. The second adventure of the Second Doctor, it helped crystalize his personality, including the reliance on disguise and subterfuge that helped set him apart from the First Doctor. It also introduced Jamie, who would turn out to be one of the Doctor’s closest companions.

Caught between warring sides at the Battle of Culloden, the Doctor affects a slight German accent and tries to play both sides as “Doctor von Wer.”
You don’t even need to know German to figure out what “Doctor von Wer” translates into…
Doctor: A gentleman at last. Doctor von Wer, at your service.
Sergeant: Doctor who?
Doctor: That’s what I said.
It’s a shame that Jamie would later create the alias “John Smith” for the Doctor, because I could have enjoyed 60 years of various aliases playing off the name “Doctor Who.”
The Underwater Menace
The very next serial, “The Underwater Menace,” had the Doctor sign a letter “Dr. W.”

“The Underwater Menace” is the first of several times the Doctor visited Atlantis. Amusingly, each time Atlantis has shown up in the series, it’s always been a different doomed underwater civilization–to the point where I now just assume that “Atlantis” was basically the underwater version of “Springfield” and there are several dozen ancient civilizations that perished at the bottom of the Atlantic Ocean.
Facing a death sentence, the Doctor sends a message to the scientist Dr. Zaroff, trying to convince his potential benefactor that he knows vital information that makes it worth keeping him alive. The plan works, and the Doctor and his companions are given a stay of execution.
Interestingly, there was no need for the Doctor to sign the letter “Dr. W.” Unlike “The Gunfighters” and “The Highlanders,” he wasn’t trying to establish an alias. It seems that some people really do know him as Doctor Who.
Honorable Mention: Sympathy from the Devil
My favorite instance of the Doctor going by “Doctor Who” (or at least something close) didn’t happen on TV. Instead, it occurred in the audio play “Sympathy for the Devil.”

In this story, the Doctor speaks with an abbot who asks him his name…
The Doctor: Sometimes, they call me Hu.
Abbot: The tiger?
The Doctor: For my courage, supposedly. Sometimes Hu.
Abbot: The fox?
The Doctor: For my cunning, they say. But I personally prefer Xue. (pronounced “who”)
Abbot: Ah…he who tends to the sick.
The Doctor: Outside China, people normally just say “The Doctor.”
I like this because it plays with the subtleties of the Chinese languages, where the same syllable can mean different things depending on its pronunciation, and also because it totally makes sense that the Doctor, somebody who loves his riddles and wordplay, would become enamored with the names he acquired in China. It gives a nice reason why he is normally known as the Doctor but sometimes likes to call himself “Doctor Who.”
After all, his name isn’t really Doctor Who…except for this times it is.