late Old English, "one who avows his religion," especially in the face of danger, but does not suffer martyrdom, from Latin confessor, agent noun from past-participle stem of confiteri "to acknowledge" (see confess). Meaning "one who hears confessions" is from mid-14c.; this properly would be Latin confessarius, but Latin confessor was being used in this sense from the 9th century. Meaning "one who admits to a crime" is from 1690s.
Edward the Confessor (c. 1003-1066, canonized 1161), the late Anglo-Saxon king, lived a pious life and died with the reputation of sanctity but does not seem to fit his title; perhaps he was so called to distinguish him from another Anglo-Saxon saint/king, Edward the Martyr (c. 962-979), who better fits his.