I think Mu-Myung is the princess he killed as the final boss at the start of the game ('Insomniac Princess').
I don't think it's a coincidence we saw the broken royalty trio statue with only the king recognizable right before she appears for a second time. The fact he didn't recognize her as an NPC and her strength means she's clearly very extra-special, not just a merchant.
Following on from that, I think the 'true ending' is probably saving her somehow/the lake kingdom, maybe she goes insane if she doesn't get enough mana cores/some offscreen event. Especially since uncovering its mysteries is his goal.