I have found that my earliest ancestors in Derbyshire UK were registered at birth and marriage as Burgin. This spelling for some lines remained to the present.
For other branches like mine the spelling changed during the 19th century to Burgoyne.
Recently I was contacted by a member of Genes Reunited from London whose earliest Burgoyne ancestor at the beginning of the 19th century was also a Burgin.
Have any other Burgoynes found a similar name change from Burgin to Burgoyne?