I heard there was a scene cut from "Space Seed" that explained how Khan remembers Chekov so well:
(entering transporter room where Khan and Marla McGivers are waiting):
"Keptin Kirk asked me to take care of beaming you down to Alpha Ceti 5."
"I should be insulted that your captain sends a mere menial to see us off!"
"Nevertheless, I am ready to transport, if you vill just step onto the platform."
"And what about our supplies?"
"I vill beam them down immediately afterward."
"Make certain you do not forget the coffee and cigarettes!"
to himself while smiling):
"Yeah, right, asshole."