There are many more records that list the name of William Birchell Peters as Birchell than that list his name as William or William B., and he was always known as Birchell in the family. His name is spelled many different ways in various records, such as Burchell, Birchel, Berchel, etc. The most accurate spelling of his name seems to be Birchell.
research notes by Jerry Bryan, 12/08/2016.