Its distribution within England is centered on Lincolnshire, followed in concentration by Lancashire, Yorkshire, Cumbria, and East Anglia.
"Occupational name from Middle English greyve, grayve, greve 'steward bailif, manorial officer who managed the lord's demense farm, headman of a town or village', a borrowing from Old Scandinavian greifi 'earl, count".
"Relationship name (in Norfolk), possibly from the rare Middle English personal name Gre(y)vy, Gre(i)ve, Old Scandinavian Greifi, *Grefe, originally a nickname meaning 'earl, count".
[1] The name likely seems to be of Scandinavian origin within England, as suggested by its distribution which corresponds largely to counties of the former Danelaw.
This suggests its most common origin being that of an occupational surname, as the Grave is the Norse derived Danelaw (from the Old Norse greifi) counterpart to the Old English Reeve (from the Old English ġerēfa).