According to Irish academic Paul Tempan, the Moira is from the title of the Earl of Moira who owned lands around Greenan, and historical papers record references to the purchase of the Ballinacor Estate and House from Francis Rawdon-Hastings, 1st Marquess of Hastings, the Earl of Moira in 1805. At the time of the purchase, the mountain would have been the Cruachán behind Ballinacor House. Tempan notes another name for the mountain, The Mottie.