the name Wallace may mean "Welsh", or possibly 'foreigner'
Lots of people were described as Wlesh, or various different forms of the word.
There was a group of Celts the Romans cvalled Volcae. (Ask Crow, he'll tell you they were Slavs). The name was borrowed into Germanic as *walkhaz to mean Celts generally.
This word gave us the modern names of Wales (and derived surnames such as Wallace), Walloons (French-speaking Belgians) and Vlachs (various Romanian groups). In Polish, the Vlachs are called Wołosi (or is that Wołosi?). Does anyone know if that is anything to do with why Italy is called Włochy, and why is that plural (if I got that right)?
Anyway, southern Scotland was in Roman times inhabited by Brythonic speakers (Welsh) rather than Goidelic speakers (Scots, Irish). So Scotland's heritage is a mixture of Welsh, Irish, Pictish (whatever that means), Roman and Saxon... and Viking... and Norman... and Polish (ha ha!)