
Is it only me or is it really cringe t call someone you like and sleep with not by their name but by their job position? Like, THHHH???

Exposure to East Asian things would make you think otherwise. Korean culture values respect, authority, status, and based on their external presentation, they also value the stage of the relationship as well (they always confess using "i like you" since "i love you" is next level; they also address their partners respectfully).
It's standard to address people based on their status (sunbae, hoobae, -ssi suffix, -nim suffix, et cetera). In this case, FL is probably referring to the CEO as "sajangnim", which sounds better than the translation tbh. And, it's standard to speak formally and respectfully to people. Speaking informally and casually happens when the parties are comfortable or agreed on it—unless you want to be brazen, rude, and start some argument idk.
FL is understandably not yet in the situation where she's comfortable to change her manner of speaking and addressing sajangnim. She's not even confident about the relationship's future yet. Both of them also never brought it up as well, probably because it's easier given their boss-subordinate relationshi (it will stir up issues if they slip up and talk casually in the office).
SPOILER
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The ML is Jiho, and Eunho will end up with Yeoryeong.
I also really love Jiho's development because of Dani—he really is becoming a better person because of and for her than he was at the beginning. whereas Chunyoung stays almost the same as a character.