a good name for a private story

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.

Perhaps 'Personal Reveries'. 'Reveries' suggests daydreams or private thoughts, and by adding 'personal', it makes it clear that these are your own, private stories. They could be about your hopes, dreams, or memories that you want to keep to yourself or share only with a very small group.

You could name it 'My Secret Chapter'. It gives a sense of mystery and privacy, like it's a part of your life that only you or a select few can access.

Well, 'Soul's Sanctuary' is a great name. It makes it seem like the private story is a safe place for your soul, where you can keep your most intimate feelings. 'Intimate Chronicles' is also suitable, as it sounds like a record of your personal experiences. And 'Private Reflections' is a straightforward and good choice, indicating that it's about your own thoughts and self - reflection.

Well, it could be 'My Secret World' or 'Hidden Chapters of My Life'.

You could name it 'My Secret Chapter'. It gives a sense of mystery and exclusivity, like it's a part of your life that only you know about or are willing to share privately.

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.

My Secret Moments.

You could name it 'My Secret Garden', which gives a sense of a personal and private space full of unique things. Another option is 'Personal Reflections', as it implies that the story is about your own thoughts and experiences. Or 'Hidden Gems', suggesting that there are precious and private things within the story.

How about 'My Secret World'? It implies that the story contains personal and hidden aspects.