Topographic name for someone who owned or lived by a meadow, or a metonymic occupational name for someone who made or sold hay, from Middle English gras, Middle High German gras "grass, pasture, grazing".
Occupational name, reduced from Gaelic greusaiche "shoemaker". A certain John Grasse alias Cordonar (Middle English cordewaner "shoemaker") is recorded in Scotland in 1539.