"Kahn" is a pretty common Indian surname. While, there might be few Hitlers left in the wold, I don't think everybdy named Kahn (or Green, for that matter) would change their names in reaction to the actions of one man.
I suspect there would have been quite an Augment witch hunt after the Eugenics Wars. And judging by reactions to Augments in Enterprise and Deep Space Nine, it would seem that Khan blood would be an instant ticket to persona non grata
status in the Federation even 300 years later. Not something any sane person would wear on their sleeve.
I don't know. According to "Space Seed," Khan was regarded by history as one of the more admirable genetic tyrants. Both Kirk and Scotty confessed to having always had a sneaking admiration for him, and Kirk specifically mentions that there were no known massacres under his reign.
One gets the impression, at least in "Space Seed," that Khan was remembered as more of a 20th Century Napoleon or Julius Caesar than a Hitler. An ambitious conqueror, yes, but not a monster.
Marla's reaction also supports that theory. It's hard to imagine that she would be swooning over "Hitler" or painting heroic portraits of him.
We should also note that, aside from Marla, nobody on the Enterprise
even recognizes him, which implies that Khan isn't exactly that
infamous centuries later.
And, for that matter, Terrell doesn't recognize Khan in the movie. And Chekov actually has to explain who Khan is. (Note that Chekov doesn't just say "It's Khan Noonien Singh!" as though that would be self-explanatory. He instead goes into a whole spiel about how Khan is "a product of late twentieth century genetic engineering," etc.)
In all, it doesn't seem like the name "Khan" is synonymous with evil in Kirk's time. And, indeed, nobody in "Space Seed" acts as though Khan is the equivalent of Hitler or whomever.
(Oh, one more thing: If Khan was supposed to be a Hitler type, does anyone really think an American TV episode in the 1960s would have ended with the hero letting "Hitler" and his girlfriend have a second chance on a brand new world? I think not . . . .)