McInerney, Mac an Airchinnigh A Gaelic surname meaning ‘son of the erenagh’. A sept of Roscommon, a branch of the ó Branáin who were erenagh of St. Patrick’s church at Elphin. A sept of Thuas Mhumhan (Thomand) who were based in the parish of Ballysally. In 1890 McInerney was numerous in Clare, it was also to be found in Limerick, and the estimated number of bearers was 2,867 (including variants). In the United States it is the 8,906th most numerous surname with an estimated 2,750 bearers.