In reply to G8ADD:
"The name seems to derive from both a Welsh and a Gaelic word for a small hut or cottage but “both” and “booth” in Norse and Old English respectively had a similar meaning. "
Bwthyn ! said the little Welsh voice in my head all of a sudden to my surprise. I wonder what the Gaelic word is? A Bwthyn would be the hut at Llyn Arenig where you could overnight before climbing GW/NW-011 [but bring your own firewood to burn in the grate].