Just FYI, the surname “White” comes from the same place that “Black” does, whitesmithing and blacksmithing. If we’re being pedantic, we have to assume that Snow White’s ancestor worked in tin and silver and not assume that she was given an arbitrary surname because her parents somehow knew she would have alabaster white skin.
I don’t know if this is a translation problem or people never read the story, but the story literally goes „Bald darauf bekam sie ein Töchterlein, das war so weiß wie Schnee, so rot wie Blut, und so schwarzhaarig wie Ebenholz, und ward darum das Schneewittchen genannt.“ i.e. “her daughter was as white as snow […], and that’s why she was called Snow White”. There’s absolutely no ambiguity why she was called the way she was.