Neilson
Neilson—This name is the anglicised form of McNeill. It is found in Scotland, Ulster and the Isle of Man. Within latter times it has been changed to Nelson, a name of the same origin. In passing, I may mention that McNeill has also been rendered M'Neillage and McNeillaige; the Gaelic form of which is Mac Neill-Og, meaning "Young McNeill." See Nelson.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees