In the traditional Snow White story, the dwarfs are often named Doc, Grumpy, Happy, Sleepy, Bashful, Sneezy, and Dopey. Snow White doesn't have a different 'hidden' name in the original story, she is simply Snow White.
Well, in the story of Snow White and the Seven Dwarfs, the dwarfs are named quite interestingly. Doc is like the leader, often seen as the smartest. Grumpy is always in a bit of a bad mood. Happy is, as his name implies, always cheerful. Sleepy is constantly tired. Bashful is shy. Sneezy has a sneezing problem. And Dopey is the silly one. Their names really help to bring out their distinct personalities in the story.
Most likely not. The names of Snow White and the dwarfs were created by the storytellers for the purpose of the fairy tale. They are fictional names to bring the characters to life.
The 'snow white dwarfs story' could potentially be a new and unique interpretation of the classic Snow White tale. Maybe it focuses more on the dwarfs' backstories, like where they came from, how they found their cottage in the forest, and their relationships with each other and with Snow White. It could also explore how they interact with the magic in the story, like the magic mirror or the queen's spells.