Original: This would probably explain the origin of Bunyan's last name since "Bonyenne" is a colloquial French-Canadian expression of surprise and astonishment meaning "Good Grief" or "My Goodness".
Simplified: This would explain why Paul Bunyan's last name is "Bunyan", because "Bunyan" sounds like the French-Canadian slang word "Bonyenne", which is something that they might say when they are surprised, like how people who speak English might say "Good Grief" or "My Goodness".