'Preston' probably means the farm belonging to the priest.
It probably joins Old English words for priest and farm; the name may go back to an estate that King Offa of Mercia gave to Abbot Stidberht in 767. Preston was first mentioned in 1220. The station opened in 1908 as Preston Road Halt for Uxendon and Kenton, helped by pressure from the shooting club at Uxendon Farm, used for Olympic clay pigeon shooting that year.