I'm totally down with Billie as a girl's name! My stock combo (for the moment) is Billie Charlotte.
My stepmom had an aunt (Grandma's sister) who passed away a while ago, and for years I misheard her name as "Aunt Bea" and thought her name was Beatrice - until I saw a labelled picture of Grandma and her two older sisters, Veneta (technically a half-sister) and Billie Rose. That's when I realized "B" had referred to her first initial. Billie Rose struck me as cutely retro.
I have a feeling Billie Eilish will eventually cause the name to trend. Even if people aren't explicitly naming their daughters after her, they'll have heard her name enough that the sound may grow on them.
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