Personal Chronicles. This name gives the idea that it's about your own personal stories that are only for you or a select few. It has a bit of a classic and timeless feel to it.
Some names that might work are 'Hidden Tales', 'Exclusive Snaps', or 'Secret Snap Diaries'. These names give the idea that the story is only for a select few or for your own private viewing.
Hidden Gems. It implies that the content in the private snap story is something special, like precious gems that are hidden away from the public eye. It could be used for snaps that include unique memories, private jokes, or exclusive events that only a select few are supposed to see.
How about 'Behind the Lens'? It implies that there are hidden or unseen aspects of your life that you're sharing. Or 'Snapshots of Me' which focuses on it being about you and your experiences.
You could call it 'The Enchanted Forest Adventure'. It gives the idea of a story set in a forest full of magic and mystery. Maybe the main character is a young explorer who stumbles upon this forest and has to face various challenges and meet strange creatures.
Consider 'The Hidden Doorway'. This title is very evocative. It could lead to a story where there is a door that is hidden in an ordinary place, like in the back of a closet or under a staircase. When the main character discovers this door, they enter a whole new world full of different rules and beings. For example, it could be a world where animals can talk and magic is real. The character then has to navigate this new world and figure out how to get back home if they want to.