The story
Wyre is believed to mean Wyre Forest, although it is some distance away. Piddle relates to the local Piddle Brook. Wyre Halt railway station, closed in 1966, avoided the Piddle affix, presumably due to the use of piddle (“urine”); the village and parish council appear to be unabashed by that association.
Etymology from Wiktionary, CC BY-SA 4.0.