According to the Dictionary of American Family Names, it could be English or German in origin. In English it is from a pet form the Old English personal name Budda. In German, it's possibly from a shortened form of a North German farm name such as Buddenbrock, Buddendiek, or Buddensiek, all containing the element budde(n) ‘morass’, ‘bog’. It appears most of the Buddens seem to originate in England, though there are good portion that came to America from Ireland or Germany. Distribution of Budden families from England and Wales in 1891 from Ancestry.com show most Buddens were in Dorsetshire, Hampshire and London.