See biography by I. Mortimer (2006).
One version is that it derives from "Mortemer", site of the Cistercian Abbaye de Mortemer at Lisors between Les Andelys and Évreux in Normandy. The land was gifted to the Cistercians by Henry II in the 1180s. Finding the land to be marsh-land (in old french, 'dead water' or "Morte Mer"), the monks dug out a large drainage lake and built the Abbaye de Mortemer. The ruins and lake can still be visited, and the later XVIth century Abbey hosts tours.
The village of Mortemer-sur-Eaulne further north in the Seine-Maritime area bears the same name, but it is unclear if the name predates the Abbey at Lisors.
Another version, allegedly dating from the Victorian era, attributes the name to a Norman Knight who fought in the crusades and was distinguished in battle by the shores of the Dead Sea, but this is unsubstantiated and almost certainly a romanticised myth.