Hi,
According to the marriage record the father's name was Arthur. The family search site shows an Arthur Walsh and a Margaret Duffin registered a son, Hugh in Broughshane ,Ballymena but the date was 8 Mar 1869. The site also shows a Hugh WELSH born to Arthur Welsh and Margaret McAlister also in Ballymena on 11 Mar 1876. The marriage for this Hugh and Margaret gives the name as WALSH. The marriages for both Arthur Walsh/welsh took place in Roman Catholic churches.
Regards