It was originally a surname, but so were quite a few other names, such as
Leslie, which became common to see as first names for girls.
Beverly or
Beverley has been established as a first name for girls for so long now that I don't think that anyone is going to think "surname" upon seeing it.
Back in the 1960s, when I was a child, there was a neighborhood girl named
Beverly to whom all the other kids in the neighborhood were mean, and one of the things we used to do was call her "
Beverly Hillbillies." I don't think that reference is going to come so easily to children today, though, and of course, it wasn't her name itself that caused us to tease her, we were going to tease her anyway, so we hit upon her name as one way to do it.
I don't like the name, in any case. It's the first syllable that causes me to dislike it, the second and third syllables are actually quite nice.