origins
Ashkenazi Jewish
Americanized spelling of Ashkenazic Jewish S(c)hor(r) or Szor, variants of Schauer.
German and Austrian: occupational name for an official inspector, for example the official overseer of a market, from Middle High German schouwer, an agent derivative of schouwen ‘to inspect’.
Certain branches of the Shore, Scher, Schur, etc., families, are "Levi" family names - either because members of the tribe of Levi opened the gate ( sha'ar ) of the Bait haMikdash (Holy Temple in Jerusalem) or because they sang songs ( shir ) during the Service.