In the 1937 film Snow White, the Queen asks the Magic Mirror "who is the fairest of them all":
Queen: Slave in the magic mirror, come from the farthest space, through wind and darkness I summon thee. Speak! Let me see thy face.
Magic Mirror: What wouldst thou know, my Queen?
Queen: Magic mirror on the wall, who is the fairest one of all?
Magic Mirror: Famed is thy beauty, Majesty. But hold, a lovely maid I see. Rags cannot hide her gentle grace. Alas, she is more fair than thee.
Queen: Alas for her! Reveal her name.
Magic Mirror: Lips red as the rose. Hair black as ebony. Skin white as snow.
Queen: Snow White!
Despite demanding a name, the mirror remains cryptic, giving only more description. However, the Queen is still able to determine who it is.
Having recently re-watched the film, I don't see where the Queen would have encountered Snow White well enough to know her name. The first time we see her she is a maid in a castle, but no link is made that this is the Queen's castle or otherwise.
In the film, how does the Queen make this logical leap?