Why Dr Spock?
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Dr Spock was a [**real person**](https://en.wikipedia.org/wiki/Benjamin_Spock), an American pediatrician whose book *Baby and Child Care*, published in 1946, is one of the best-sellers of all time. This Benjamin Spock had a PhD, unlike Star-Trek Spock, and is usually referred to as "Dr Spock".

Quoting from [Wikipedia](https://en.wikipedia.org/wiki/Spock) (sourced from the book *The Making of Star Trek*):

> Roddenberry sought an alien-sounding name when he created "Spock", and did not know until later of Dr. Benjamin Spock, the pediatrician and author.

Quoting (again) from [this discussion](https://groups.google.com/forum/#!topic/alt.startrek.vulcan/irTRKTNo2Ak):

> When Gene Roddenberry was informed that the name of his Vulcan was of a real
person it was too late to change it.  Star Trek and the baby-doctor both
emerged into the public eye about the same time and some people who knew little
of either confused the two into one.

This confusion has led to people - including some [famous people](http://www.dailymail.co.uk/news/article-2976068/She-just-mis-Spock-Kirstie-Alley-mocked-Star-Trek-fans-confusing-Leonard-Nimoy-s-character-namesake-child-psychologist-tribute-tweet.html) - calling Star-Trek Spock "Dr Spock" by mistake.
<hr>
When did it start?
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An article [here](http://henryjenkins.org/2007/08/the_new_mr_spock.html), mainly about *Dr* Spock, says (emphasis mine):

> Leonard Nemoy [sic] struggled **his whole career** with people who confused Dr. and Mr. Spock, a confusion which normally resulted in an arch of his eyebrow.

So it looks as though the confusion goes right the way back to the start of Star Trek TOS. Indeed, the Star Trek writer Leonard Weinstein once [said](https://books.google.co.uk/books?id=_Enmn8Vs688C&pg=PA12-IA46&lpg=PA12-IA46&dq=star+trek+%22dr+spock%22+origin+of+confusion&source=bl&ots=UhHZ0-_qOG&sig=Oqizc0pRF3hLzrnQhf3R4tlTL68&hl=en&sa=X&ved=0CFgQ6AEwCWoVChMIgeb0tb_gxwIVw78UCh3IAAln#v=onepage&q=star%20trek%20%22dr%20spock%22%20origin%20of%20confusion&f=false):

> I was about seven when Alan Shepard became the first non-canine, non-chimp American astronaut in 1961 (fast becoming ancient history!). I knew nothing about science fiction, but real space exploration captured my imagination right from the start. Five years later, as NASA advanced from Mercury to Gemini, _Star Trek_ started without me. I don't know what I was watching in September '66, but it wasn't _Star Trek_. I heard my junior-high pals talk about it at the lunch table, but I must not have been paying close attention, because **I confused Mr. Spock with Dr. Spock** and Dr. Spock with Dr. Smith from _Lost in Space_. And what little I'd seen of _Lost in Space_ had not impressed me, and I hadn't even noticed _Star Trek_. But my friends kept talking about it, so midway through the first season, I watched _Star Trek_ myself.

This proves that the confusion dates back to the very first season of Star Trek TOS.