Several surname etymology books mention the surname BARLOW without any hint of a Norman origin.
The difficulty of tracing back a male line of descent to Norman origins via the battle of Hastings is discussed on p. 37 of “The Story of Surnames,” by L[eslie] G. Pine, published 1966. He says there are less than 30 Norman invaders known to us, including some who died without issue.
He says Domesday Book was compiled 20 years after the battle. That the colonists in Domesday need not be the same people as the warriors at Hastings. ". . . the men who were in the first wave at the Normandy beaches in 1944 [D-Day] did not normally hold the executive posts in the commissions which governed the liberated countries some years later."
Reg Niles RegNMINiles@cs.com