The origin of the name Berriman
The surnames Berryman and Berriman are common around St Buryans in Cornwall, so it is possible that the Cornish Berry(i)mans took their name from "St Buryans man". However, a recent DNA study suggests that the Berrymans, along with many other old Cornish families, are of English, not Celtic, origin. It is possible, therefore, that the Cornish and Gloucestershire Berrymans are related.
This was St Buryan a few years ago: 
The name may be derived from the word "Bury". Here is a description from: Hanks and Hodges, 1988:
English: habitation name or topographic name, ultimately from the dative case, byrig, of Old English burh fortified place, originally used after a preposition (e.g. Richard atte Bery). As inflections were lost in Middle English, derivatives of the Old English dative replaced the Old English nominative, the word taking forms such as biri, berie, and burie. In Middle English this word acquired two different senses, both of which have given rise to surnames. In late Old English and early Middle English it denoted a fortified manor house, and the surname was used for someone who lived near a manor house or as an occupational name for someone employed in a manor house. The word also came to denote a fortified town, and is therefore an habitation name from any of various places so named. From this sense developed the modern English word borough. The surname Bury is especially common in Lancashire, where it is no doubt mainly if not exclusively an habitation name from the town of this name, but may also be from various other, less important, places similarly named.
Variants: Atberry, Atbury, Atterbury (with fused preposition); Berriman, Berryman (chiefly Devon); Berry