According to Wikipedia the origin of the name is almost certainly Norman, but the details are disputed.

One version is that it derives from 'Mortemer', site of the Cistercian Abbaye de Mortemer at Lisors near Lyons-la-Fort and close to Rouen in Normandy. The land was granted to the Cistercians by Henry II in the 1180s. Finding the land to be a marshy-land of the Lyons Forest around the running Fouillebroc Stream, 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 16th century Abbey hosts tours.

There are two possible explanations: first, a small pond must have already existed before the land was given to the monks and have already called Mortemer like the two other Mortemer, because the word mer 'pond' was not used anymore beyond the Xth century. This word is only attested in North-Western France and of frankish or saxon origin mari / meri 'mere', 'lake' (in Cambremer, Blingemer, etc..); mort(e) 'dead' is also quite common to mean 'stagnant' (in Port-Mort 'the port with stagnant water', Morteau 'dead water', etc.). Second, the monks could have given the name Mortemer to their drainage lake to remember the other Mortemer for any kind of reason we don't know, making a pun at the same time with Mer Morte 'Dead Sea'.

Certainly the historical English connections go back as far as William the Conqueror, that particular line possibly dying out with Edmund Mortimer 5th Earl of March d1425.