His mother, Máire Ní Dheasmhumhnaigh (born 1888), also known as Mary Desmond, was the daughter of Dónal Ó Deasmhumhnaigh (born 1851) and Nóra Ní Bhriain of Kinsale. Several members of Kieron's family pursued careers in the arts. His sister Neasa Ní Annracháin was a stalwart of the Raidió Éireann Players, while his brother, Fachtna, was director of music at the station, and a second sister, Bláithín Ní Annracháin, played the harp with the National Symphony Orchestra. Following his family's move to Dublin, Moore attended Coláiste Mhuire, an Irish-language school.