Interesting. I also know that several European immigrant families anglicized their surnames to make it easier to blend in North America. One of the easiest to remember is, although it was for his stage name is Alex Lifeson of Rush, Lifeson being the translation of the Slavic Zivojinovic as I am given to understand.
I had guessed that it could be that in your case as well because I had never heard of a UK surname Barefoot before. Cheers!