In the UK when we think of trolls, the three Billy Goats Gruff (De tre bukkene Bruse ), which is a Norwegian folk tale, comes to mind. Essentially, dim bridge troll outwitted by 3 smart male goats of ascending sizes.
To my mind when I see an umlaut I reckon the person is a German speaker, studied German at Uni or it is just a lucky stab on Google. The upshot is I don't fence with them as their level of certainty is greater than mine and finding it on the keyboard is a pain. Anybody who has had or has kids would know the Cat in the Hat and how the eponymous cat translates hat into many languages:
"cat, hat; in French, chat, chapeau
in Spanish, el gato in a sombrero
in German I'm a Katze in a Hut, and don't you know,
I'm a guanka in a bunkaquank in Eskimo"
I believe the Cat's hat is a Hut not a Mütze so where to draw the line seems clear.