And none of this addresses the question of why Starfleet didn't have a record of Khan's presence in this system. I have a hard time believing Kirk would've been so criminally irresponsible as to leave Starfleet unaware of the fact that there was a potentially dangerous population of superhuman criminals living in the system and that they should probably be left alone.
Who says they didn't? I agree that Kirk wouldn't have avoided sharing the incident with Starfleet, but it's possible Khan's whereabouts were limited to the senior staff and select admirals at Starfleet Command. Lower-ranking personnel may not have been privy to where the Enterprise
was going once Kirk decided what to do with Khan and his people.
Chekov does make a statement suggesting he
knew where Khan's people were located. He says, "On Ceti Alpha V, there was life, a fair chance..." He says nothing about anyone else who was aboard the ship, however. I don't know that Kyle would've been told anything. He could certainly have operated the transporter without knowing the name of the planet onto which he was beaming Khan. As for why Chekov forgot, who knows? It's Chekov.