Search:

checking my three books :) :
All three have Уотсон. The earliest of them is of 1956 with Корней Чуковский as a translation editor. So I think the popularity of "Ватсон" vs "Уотсон" is more a movie...

Уильям or Вильям. Often it depends on tradition. For example Bruce Willis is traditionaly transliterated as Брюс Уиллис but Doyle's Doctor Watson is usually written as "доктор Ватсон".