In the Disney film, there's no explanation for why Snow White gets that name, other than her being, well, white. It's just one of those fairy tale names, it doesn't have to make sense, right? But it turns out that the Brothers Grimm's original version of the tale actually gives her name an origin story.
Originally, Snow White's mother is sewing while watching snow fall at the castle when she accidentally pricks herself with her needle. The drops of blood lands on the fresh snow (apparently the window — said to have a frame of ebony wood — was open, which sounds sort of uncomfortable if it's snowing) and causes her mother to say, "If only I had a child as white as snow, lips as red as blood, and as black as the wood in this frame." That's a pretty creepy thing to say out of nowhere, but hey, fairy tale parents are weird.
This scene doesn't appear in the Disney version at all, but they do refer to it. The Magic Mirror, when first describing Snow White, says she has "lips as red as rose, hair as black as ebony, skin as white as snow." As you might have noticed, they skip over the whole red as blood part, making it much tamer with the whole flower analogy.
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