I have all dictionaries of Polish but etymological one. Polish name for Carpathian mountains is just Karpaty , I don't have an idea what is the origin, but maybe karpa , which means tne part of a plant or a tree, that is under ground but not simply the root, it can also mean, that what remains after a tree is torn off and cuted ( this thing with the roots).

I like your question. I must check it at school on friday.