I like how you corrected Spock after mockery but not McCoy. Also, how could you leave out Scotty?
Granted, if you grew up on the Next Generation or Voyager or DS9 (which gets way more hate than it should) then you might not know Kirk or Spock or TOS outside of the countless references they get everywhere else (e.g. "Dammit <name>, I'm a <blank> not a <blank>" that pop up in other popular media). At least at first.
Considering that the new movies are all about the first generation cast, even the casual fan knows about them. They might not know who William Shatner and Leonard Nimoy are or who George Takei is outside of his wonderful facebook posts. They might not know that Nichelle Nichols had to be hired as a guest star for each episode because the studios wouldn't hire a black actress full time. They might not know that she got a lot of hate mail. They might not know that Shatner and Nichols purposely flubbed their lines in all the cuts so television networks would have to show the first interracial kiss on television... but people who are new to Trek fandom certainly know who Kirk and Spock are.