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There are more possible derivations of the German name Moser:
1. from various place-names like Moos or Moser (Bavaria, Austria),
2. same as Möser (O umlaut): "greengrocer" (from Middle Low German "mos" = cabbage, vegetables) or "mortar" from Middle Low German "moser, moyser") or again various place-names (usually containing the element "moos" = moss)
3. in a Jewish context it could be used as an equivalent to Moses

All of this is taken from:
Rosa and Volker Kohlheim (ed.): Familiennamen, Mannheim 2000 (Duden Verlag)

Andy ;—)