There may be an echo in both cross-names of the medieval legendary hero Sir Bevis of Hampton, and it may or may not be a coincidence that the site of Bewys Cross was in the tithing of Shirehampton, which was in early medieval times called simply Hampton. There is a mention in 1551 of a place called Bewehurste at Compton in the nearby parish of Almondsbury, which is of uncertain relevance.
There might be a connection between the cross-names linked to the medieval legendary hero Sir Bevis of Hampton and the location of Bewys Cross within Shirehampton. This could also relate to the mention of Bewehurste in 1551 at Compton, which is uncertain.