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.
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.
Well, a private snap story on Snapchat is like your own little exclusive album. You can add snaps to it and decide exactly who gets to see it. It's different from a regular story that might be visible to all your friends or even the public if your settings are wrong. With a private one, you're in control. You pick the people, say your closest friends or family members, and they are the only ones who can peek at what you've shared in that private story.