Funny you should ask that. We were just wondering about Japanese names for next year's Samurai games and I thought you'd be just the man to ask with the expert knowledge shown on your web site and blog?
Unfortunately the Japanese don't really have a 'b' in the same way that we do but I've found a couple of names that begin with it...
Baba
Baisotei
Bando
Bunya
There are no names (out of about approx 900-1000 names) that remotely sound like it

Did a bit of digging and found this from the House of names website...
The name Bickley is of Anglo-Saxon origin and came from when the family lived in the town of Bickley in the county of Devon. This place-name is derived from the Anglo Saxon personal name Bicca meaning pickaxe, and the Old English word leigh, meaning wooded area.
So if the elements of the name are loosely switched to Japanese you end up with
Ono for pickaxe and
Mori for wood (or forest) or Onomori

All rather tenuous but at least it's something near correct

cheers
James