Until recently Jysk was called Dänisches Bettenlager (danish bed warehouse), probably because Jysk doesn't exactly roll off the tongue for German speakers.
For an English speaker to pronounce "Jysk" something approaching the correct way, they should read something between "Yusk" and "Yoosk". For a German maybe "Jüsk".
Until recently, JYSK was also called Jysk Sengetøjslager (= bettenlager) in Denmark. I think the rebranding to JYSK was just about making the name shorter and the same everywhere.