From Chicklade And Pertwood, A Short Parish History by E.R. Barty, M.A., Chicklade, Old Rectory, first published December 1955:
PERTWOOD
Perteworde (1086)
Purtwerthe (1270)
Pert worthy (1411)
Pertewodde (1535)
“This name must remain an unsolved problem.â€
A possible association is with the Welsh perth-bwash (brake) British perta (wood; the source of Perth, Scotland).
“Place Names of Wiltshire,†English Place Name Society, Vol. XVI. C.U.P. 1939).