In Jewish mythology (the Kabbala?), if I remember right, Lillith was originally created to be Adam’s wife (before Eve) but instead sinned before meeting Adam and became the queen of Hell, Satan’ wife.
It is not a name I’d give to a daughter.
I could be wrong
Wasn’t it also the name of Kelsey Grammers characters wife / girl friend who was the classic gimme, I want, lets go now ball breaker in the TV sitcom Fraiser ?
Fitting name for her ...... “Lillith”
“ADAM and EVE: Lilith, be gone!”