The association with “trees” is probably spot on.
I found this little tidbit, looking at a whim:
Berky Pronunciation of Berky as a name for boys is of Old English origin, and the meaning of Berky is “birch tree meadow”. Berky is an alternate spelling of Barclay (Scottish, Old English): place name for Berkeley in Gloucestershire.
STARTS WITH Be-
ASSOCIATED WITH old english, tree, meadow
Close enough to be interesting...
It fits, trees have bark, and pronouncing it “barkshur” isn’t unheard of. 😊 In my misspent youth, I read (possibly in Bulfinch’s) that the root of our transliteration “druid” is “daru vid”, which means, “to know the oak”. Hey, winters are long, much of the island was rural in ancient times...