Mr, Plankton name jokes gone over my head or Korean inside joke?

I just finished Mr. Plankton (incredibly sad show, LOVED it) I saw it in English sub and there were a few moments where I feel like the jest wasn’t translated well or maybe I missed the punchline? I just assumed the jokes had word play in Korean that didn’t translate well when reading it in English. The ones I’m talking about is their names, Jae-mi and Eo Heung had a moment where they poked fun and each other’s name and I didn’t get it lol. I think I understand the joke in Hae Jo’s name, basically a little play on English “Hi, Joe” like in Better Call Saul where we find out Saul Goodman comes from “Its all good-man” (idk I might be reaching) Can someone explain please! Besides that I was impressed with the English caption ability to translate the puns into English meaning.