At least in the case of Cybill Shepherd, the name's most famous bearer, the name is not actually a variant of Sibyl. Rather, it is a combination of the names Cy and Bill, after her grandfather and father, respectively.
In the video game "Silent Hill", Cybil Bennett is a non-playable character that Harry Mason (the protagonist) meets in the town. She is a police officer from the neighboring town of Brahms, and the actions of the player determine her fate.