Meaning of the last name Crossman?

# English: topographic name for someone who lived by a stone cross, from Old Norse kross (see Cross 1) + Middle English man. # Altered spelling of German Crossmann or Crössmann; the first may be a habitational name from any of several places called Crossen in Saxony, Brandenburg, and East Prussia, or derived from Grossmann. The second is possibly from Middle Low German kros, krüs 'pitcher', and hence a metonymic occupational name for maker of these; alternatively it may be a metonymic occupational name for a butcher, from Middle High German kroese 'tripe'