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I'm only learning Danish.

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 :-)