The same as the first name, "English: from a pet form of the Middle English personal name Boye" Source: Dictionary of American Family Names ©2013, Oxford University Press. As for Boye itself: "English, North
German,
Dutch, Frisian, and Danish: from a Germanic personal name, Boio or Bogo, of uncertain origin. It may represent a variant of Bothe, with the regular Low
German loss of the dental between vowels, but a cognate name appears to have existed in Old English (see
Boyce), where this feature does not occur. Boje is still in use as a personal name in Friesland.…
Source: Dictionary of American Family Names ©2013, Oxford University Press
The Welsh ancestry is neither here no there. Welsh was suppressed for many years, so it's not unusual to see Welsh people with English surnames. Despite it's
Saxon origins, the highest concentrations outside
London of Boye families were in Cumberland,
Devon and Gloucestershire.