Muiredach (Old Irish), Muireadhach or Muireach, anglicized variously to Murdoch, Murtagh, Murray, Murdac, Mordacq and other forms, is a Goidelic name (meaning "chieftain") popular in Scotland and Ireland in the Middle Ages:

• Muiredach Bolgrach, mythological Irish king
• Muiredach Tirech, legendary high-king of Ireland
• Muiredach mac Eógain (died 489), legendary early king of Ailech
• Muiredach Muinderg (died 489), legendary king of the Ulaid
• Muiredach of Killala, reputed early Irish saint
• Muiredach Muillethan (died 702), king of Connaught
• Muiredach mac Ainbcellaig (died c. 770), king of Dál Riata
• Muiredach mac Murchado (died 760), king of Leinster
• Muiredach mac Brain (died 818) (8th-century–818), king of Leinster
• Muiredach mac Ruadrach (8th-century–829), king of Leinster
• Muiredach mac Eochada (died 839), king of the Ulaid
• Muiredach mac Brain (died 885), king of Munster
• Muiredach mac Eochocáin (died 895), king of the Ulaid
• Muireadhach Ua Carthaigh (died 1067), Chief Poet of Connacht
• Muireadhach Ua Dubhthaigh, Archbishop of Connacht
• Muireadhach Ua Flaithbheartaigh (died 1121), King of Iar Connacht
• Muiredach (ealdorman) (fl. 958–963), ealdorman
• Muireadhach I, Earl of Menteith (fl. 12th-century–13th-century), Scottish mormaer
• Muireadhach Albanach (fl. early 12th-century–13th-century), Gaelic poet and crusader
• Muireadhach II, Earl of Menteith (died c. 1230), Scottish mormaer
• Muireadhach III, Earl of Menteith (died 1332), Scottish mormaer
• Muireadhach of Inchaffray (died 1340s), Scottish abbot
• Muireadhach Sdíbhard or Muireadhach IV, Earl of Menteith (died 1425), Scottish prince
• Muredach Dynan (1938-2021), educationalist