Lilith - Female Vampire Name

A complex figure, Lilith was born in the Jewish tradition from a Sumerian vampire-demon figure, also known as Lillu, Ardat Lili, and Irdu Lili. Lilith was known as the first wife of Adam, who left him to go dwell in the desert. She became a demoness and the mother of all demons (who were called, in the plural, "Lilith" as well), and attacked infants, sucking their blood and strangling them.

Eventually she and her demons lost this vampiric quality and were merely associated with the untimely death of any young child or baby. It can be hypothesized that this Lilith legend, making it's way into Europe after the Jewish Diaspora of 70 A.D., is the basis for the other female, vampire-like demonesses who attacked children, such as the Bruja of Spain, or the Lamia of Greece. (Hebrew)

Information from:
The Natural History of the Vampire
The Vampire Book: The Encyclopedia of the Undead