Well... [SPOILERS]
In the good route, she literally asks him, when they are alone (at the reconciliation scene, after their fight). There he says his name is Rupert. You have the choice to betray him by choosing that name (and then you get the "Betrayal" BAD END).
And even after that, when he decides to sacrifice himself to set her free, by "drunkenly" revealing his name in a song, you have the choice to use that name and Rupert. Both get you the Betrayal BAD END.
BUT! If you don't use either name, instead choosing "...", what happens is that you are refusing to betray him. Instead, you/the miller's daughter makes up a name for him. It's a name that mixes up everything she knows about him: that he's a rump (=rumpel aka an "ass"), that he uses stilts, and that he has soft skin...
Rumpel-stilt-skin.
She's not calling him by his name: she's calling him *a* name. It's a inner joke between the two after everything they have lived together :)
I'm glad you mention this to me. Now I realize that part of the story can be made a bit clearer. I'll see about adding this explanation in the next update. Thanks
And thank you for the thoughtful review. It's nice to hear at least there's somebody that could play the mini-game without issue X'D