Bygrave

This ancient name is of Anglo-Saxon origin, and has the unusual distinction of being first recorded some seventy years before the Domesday Book of 1086.

As a surname, Bygrave may be either locational or topographical in origin;

Locationally, it derives from the place called Bygrave near Baldock in Hertfordshire, which is recorded as "Bigrafan" in the Saxon Chartulary of 973, and as "Bigrave" in Domesday. The place is so called from the Olde English pre 7th Century "bi Grafan", (the place) by the ditch, from "grafa", ditch, a derivative of "grafan", to dig; in Middle English this became Bygrave.
As a topographical surname, Bygrave denoted residence by a ditch or dike, probably dug for defensive purposes