For private stories, you might consider names like 'Intimate Reflections'. This name implies that the stories are personal and close to the heart. Another option is 'Secret Scribbles', which has a bit of a fun and mysterious feel. 'Private Reveries' is also a nice name. It suggests that the stories are like daydreams or personal thoughts that are only for you or a select few.
The best names often draw from the core of the story. For example, if it's about personal growth, 'The Path to Self-Discovery' could be good. Or for a fantasy story, 'The Magic Within the Shadows' might be fitting.
Well, 'Personal Pics Parade' makes it seem like a fun collection of your personal pictures in the snap stories. 'Secret Snap Selections' gives the idea that you've carefully chosen these snaps for a private viewing. And 'Private Photo Pile' is like a little stash of photos that are only for a special group or just for you. These names can make your private snap stories more interesting and unique.
You could name it 'My Secret Chapter'. It gives a sense of mystery and privacy. Another option is 'Personal Chronicles', which implies it's a record of personal experiences that are meant to be private. Or 'Hidden Tales' as it clearly shows that the stories within are hidden or private.