Private Perspectives. It implies that the snap story will show things from your own private point of view, whether it's your thoughts, experiences, or just little snippets of your day that you don't want to share publicly.
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.
You could name it 'My Secret Chapter'. This gives a sense of it being something personal and exclusive, like a chapter in your life that only you know about.
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 go for something like 'My Secret Snap World' or 'Snap Tales of Me'.
You could call it 'My Secret Chronicles'. It gives a sense of it being a personal and private account of events in your life. Another option is 'Hidden Tales', which implies that the stories within are not meant for public consumption. And 'Personal Reveries' also works well as it suggests private thoughts and experiences.