DOM, applied to the Benedictine Abbots, for example that of Santo Domingo de Silos in Burgos, or other religious orders, consists of the initials of Dominum Optimus Maximum, freely translated would, more or less, " the best or maximum representative of the religious community to Dios " i.e., the head or representative of the community before God... Although I still remember the Latin declensions, not is both latin as to make sure that Latino cases that I expose are accurate. I don't know if it is Maximus Dominum or Dominus and Maximum, but appears to be the origin of DOM is this.