Haha :D
Yeah, I know. A danish speaking linguist friend of mine told the exact same thing the other day with very similar reasoning as yours. This name stuck with me for a long time as an idea if I ever want to start a _fake_ nordic brand - and I think for _that_ it’s perfect :D
I decided the start of the name is from the far north (Norrland) dialect of Swedish, since they pronounce the Swedish SJ sound as SH.
The letter Ø and especially clusters of pointless, not-pronounced consonants at the end of the word is very much Danish, so we can assume the second half is spoken like Danish øen, "the island" (two syllables, ø-en), and ignore the rgh :-)