I'm sorry, but that logic is very flawed. There is absolutely no evidence that the obsolete verb form "woll" was ever confused with the name "
Will". The forms Woll and Boll (as given names) were simply not registered, let alone shortened to
Bo (was
Noll shortened to No or Moll to
Mo?). And following that logic, wouldn't Wo be a name as well?
Can you find any examples of the nickname
Bo being used before modern times (including the time when the word woll was used), or it being used in Britain at all? Keep in mind that multiple nicknames were indeed used for
William - Wilk,
Wilkin,
Wilkie,
Wilmot - that now survive as surnames.
In short, your theory makes no sense whatsoever. This is the name facts board, and we should focus on facts rather than folk etymology or wishful thinking.