From the name (Greek Sibylla or Sybilla, with confusion over the vowels from an early period) of a class of ancient prophetesses inspired by Apollo. According to medieval theology, they were pagans denied the knowledge of Christ but blessed by God with some insight into things to come and accordingly admitted to heaven. It was thus regarded as a respectable name to be borne by Christians. This name was introduced to England by the Normans and enjoyed considerable popularity in the Middle Ages.
Polish (Sokół), Czech, Slovak, Belorussian, and Jewish (eastern Ashkenazic): from Belorussian and Czech sokol, Polish sokół ‘falcon’, hence a metonymic occupational name for a falconer, or a nickname for someone thought to resemble a falcon in some way. As a Jewish name it is generally ornamental.