Proudman
Proudman—The name is the anglicised form of O'Dempsey (O'Díomasaigh) and M'Gimpsey (Mac Dhíomasaigh), the latter name being common in North County Down, from diomas, proud.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees