Poekilopleuron is known from a partial skeleton discovered by Jacques Amand Eudes-Deslongchamps in July 1835 near La Maladrerie in Normandy, France, in a layer of the Calcaire de Caen. This skeleton, part of the collection of the Musée de la Facultée des Sciences de Caen, was in 1944 destroyed during the Battle of Caen in World War II, and the taxon has since had to be studied on the basis of cast replicas. One set is present in the Muséum National d'Histoire Naturelle in Paris with inventory number MNHN 1897-2, a second in the Yale Peabody Museum, YPM 4938. The remains consisted of caudal vertebrae, cervical ribs, ribs, gastralia or belly ribs, a forelimb and a hindlimb.
Eudes-Deslongchamps named the type species Poekilopleuron bucklandii in 1837 or 1838. The generic name is derived from Greek poikilos, "varied", and pleuron, "rib", a reference to the three types of rib present. The specific name, honouring William Buckland, was deliberately identical to that of Megalosaurus bucklandii. Eudes-Deslongchamps thought the specimen might well be proven to belong to this earlier named species; if so, merely the generic name would have to be changed. Indeed, following 1879 Poekilopleuron was often subsumed under Megalosaurus bucklandii. Eudes-Deslongchamps' choice caused problems however, when Friedrich von Huene in 1923 concluded it was part of Megalosaurus but as a separate species within that genus. As both species carried the same epithet bucklandii, they could no longer be distinguished. Von Huene therefore renamed the species into Megalosaurus poekilopleuron. Most later authors continued using the generic name Poekilopleuron.
Another problem was caused by the fact that the name was only partially Latinised. In correct Greek it would have been "poikilopleuron", in Latin "poecilopleurum". This induced later writers to improve the spelling, leading to such variants as Poecilopleuron and Poikilopleuron (still used as late as 2006). However, the original name has priority and is valid.