But he's only supposed to work there for a short time not forever. So they don't need to know
And if you've watched a lot Kdramas and even seen how their celebrities are, a lot of them don't even mention their partners. Seeing as this is still something that imitates some aspect of real life despite the fantasy aspect, I think we can take that context into consideration with what is happening here.

I'm frustrated at how dumb the MC is, you can bash me all you guys want but he's kinda stupid in here. Can't they just release the real score between the two and who's he's really married with? Not hiding like this? Also he's not really there to work right? He's just there to get the approval of their parents and they already got it, shouldn't he resign or leave already?