According to Black's Surnames of Scotland the name 'Mordington' is derived from the 'old barony of the same name in Berwickshire, the 'tun' of a Saxon named Mordyn, Mording or Morthing. William de Mordington, the first recorded of the name, appears soon after 1200 as a vassal of the prior of Durham (Raine*).
The School & School House, Mordington
William de Morthington held part of the vill of Lamberton, c. 1235, was Chancellor of Scotland in the reign of Alexander II.... He and his son, Sir Peter de Mordingtoun, are frequent witnesses to Coldingham charters. The family appears to have ended in an heiress, Agnes, daughter of Sir Peter de Mordingtoun, who married Henry de Haliburton.'
The first mention of Mordington is in a charter of King Edgar (c.943-975) granting various lands in southern Scotland, including Mordington, to Durham cathedral; this grant was confirmed by William Rufus on 29 August 1095 (Durham University Library Archives & Special Collections, Durham Cathedral Muniments, Miscellaneous Charter 559).