Carol called Kirk to Regula One. Khan didn't know that Carol knew him, he didn't know that she would call him personally, and he didn't know that Kirk would respond in person (and if there had been another ship in the quadrant, Kirk would not have responded

). Khan was just trying to make mischief by invoking Kirk's name.
Now when Kirk stumbled across his path, he couldn't resist taking the opportunity for revenge. It was only when Kirk outsmarted him (twice) that he lost his perspective and started ranting and taking bigger risks. Despite the melodramatic performance, Khan was a much more subtle villain than Nero.
Yeah, right.
No, he couldn't have know that Dr. Marcus knew Kirk. But he dropped the name (through Chekov) to get the scientists to complain right at the source of the new 'orders'.
Khan took steps to get Kirk to come to him (or, at least, to find out 'where [he] may find' him). Or why else do you think he even allowed Carol's transmission to go through as much as it did ('it's jammed at the source' - remember?)?
Strange that you don't think my suggestions have any merit at all? I'm a lawyer and we tend to look at all the evidence and reach a conclusion on balance of probabilities. I'm doing my assessment from memory so it is quite likely that there is evidence that I've forgotten. In movies where you have too little to go on, and the possibility of plot holes being the real reason, there are often multiple explanations that are equally plausible.
So, we are back to different assumptions based on the same evidence. I've always found it odd that the transmission was jammed at source mid flow, so Khan must either have held off notifying Carol that they were taking Genesis until they were very close by or the team ran around deleting data before Carol tried to call him and she got hold of him just as Reliant entered the system (slightly more likely than NuKirk finding Spock in a cave). I think in the TWoK novelisation it was the latter, because Carol really wasn't sure that she wanted to talk to Kirk at all but it might have been a combination of both.
I also agree that Khan was taunting Kirk by dropping his name out there but I don't think he was doing it in the realistic hope that Kirk would respond immediately in person (even if he might have held out a vain hope). He had no way of knowing that Kirk would be nearby, he would have no way of knowing how many ships would come, and I don't think he would have waited around in the unlikely hope that Kirk would come if he'd found what he was looking for on the base. He wanted Kirk to find out what was going on and using his name would have flagged it to him - perhaps for a later showdown but more likely just as a taunt.