Boyd is merely the anglicised version of the Manx name - change to Boyd was very common - A W Moore notes in 1890's:
'The name BODDAGH (extinct), which is probably the same name originally as BOYD, has by the middle of the eighteenth century been in every case changed into BOYD, which latter name is still pronounced BODDAGH by a few old Manx people. BODDAGH may, however, be derived from Buadach, 'victorious,' or from the nickname Bodach, meaning 'churl.'