Now universally taken as a pet form of Jennifer. In fact, this name existed during the Middle Ages as a pet form of Jean. It is often used independently. Among many well-known bearers are the Swedish soprano Jenny Lind (originally Johanna Lind, 1820–87), the British racehorse trainer Jenny Pitman (b. 1946), and the British actress Jenny Agutter (b. 1952).
English (chiefly West Midlands): habitational name from any of various places called Woodhall, for example in Hertfordshire, Lincolnshire, North Yorkshire, and Lothian, so named from Old English wudu ‘wood’ + heall ‘hall’.