The story
Motspur is a corruption Motspur < 1865 Mosper < 1823 Motts Spur < 1627 Motes Firs, which related to the 14th century Mot family whose fields contained furze. The station was named after the nearby Motspur Farm, with Park added (matching neighbouring stations, all using the phrase to evoke high-class housing). The town quickly took the name of the station, abandoning the previous name for the area (West Barnes).
Etymology from Wiktionary, CC BY-SA 4.0.