Norris comes from an English surname which comes from Middle English norreis meaning “northerner”, referring to someone who came up from the north or perhaps in reference to a Norseman (Viking), or someone who came from Norway. It could also have been used as a topographical name for someone who lived at the north side of a house or settlement made up from Middle English north (north) and hous (house) meaning “north house” or “dweller at the north house”. Norris could also have originated as an occupational name for a wet-nurse or a foster-mother. It comes from from Old French norrice (wet-nurse) via norrir (to feed; to nourish) which comes from Latin nutrix (wet nurse, nurse) derived from PIE root *(s)neh₂- (to swim; to float). Although Norris has been used as a male name (the last time appearing in the U.S. charts in 1983), I can see it as a unisex name.