In this way, we have Jewish names like Asmodai (Book of Tobit), Azazel (Leviticus 16:8-10), or Belial (Deuteronomy 13:13, Book of Judges 19:22, Books of Samuel, part 1, 1:16, 2:12 10:27 and 25:17, and part 2 16:7 and 22:5, Books of Kings part 1, 21:10-13, Books of Chronicles, part 1, 13:7); Semitic deities like Adramelech, Baal (see Baal (demon), Baal was also a general Jewish name for a false god), Ashtaroth (derived from Astarte); Greek, Roman and Egyptian names like Bifrons (See Bifrons (demon)), Lamia, Phoenix (see Phenex); and so on. All biblical references were taken from the Vulgate.
Lilith, a female demon important in Judaism, does not count in Christian demonology. However, the newer generation of demonologists (and some modern exorcists/deliverance counsellors) recognize Lilith as a general demon, the argument being that if other Judaic demons exist in Christian demonology, so should Lilith as well, introducing her as the wife of Samael, and as a princess and queen of Hell. Also, from the aforementioned 'everything other than God and His angels, if spirit, is demon' vein of reasoning - we find valid logical reasoning for there being a 'Lilith demon' - if simply to create confusion and add validity to the following of Lilith as deity.
Lucifer, Beelzebub and Satan, were originally one Devil who were transmogrified into three different characters by demonology and the Devil remained as such. Beelzebub was a separate entity in Judaism, later appearing as a fallen angel, and Satan is the leader of fallen angels: while Lucifer was originally an unnamed angel, the one who talked Satan into joining him in the rebellion. Whether all three (as well as other names such as Baal) are considered the same being or different depends on opinion.
Thus there is little agreement on who is whom, for many names that originally were only one being have been separated into several entities. Others have been "created" by people, like Sonnilon, Olivier (demon), Raum, etc. Many demons have several spellings of their names, not all of them with a valid fundament.
Some of these demons are mentioned in the bible, but have no official names, such as the Raging Demon, or some of the demons that were cast out by Christians during the time of the New Testament, or by Jesus Christ.
Also, many deliverance counselors and exorcists in modern times, such as Dr. Ed Murphy in his book "The Handbook For Spiritual Warfare", cite examples of demons named after the afflictions they cause, or the effect they produce. In his book, Dr. Murphy retells his encounters with multiple demons manifest in a lady named Betty, naming themselves through use of her vocal cords, with names such as "Hellbent" (its purpose was to ensure Betty's place in Hell (although it was defeated)); "Unbelief" (purposed to inspire exactly what it's named for) and "Destroyer" (meant to destroy the victim's spirit).