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...
Modern English speakers took the names from French Normans trying to speak place names used by Norse speaking Vikings, whose poorly pronounced and Norse accented place names were learned from their Anglo Saxon Wives using Old West Saxon pronunciations of the original Latin and Celtic place names.
English! A Fun two millenia old Linguistic Pachenko Game!