I think 'Hidden Moments' would be a great name. It suggests that the story contains special, maybe even private, times that not everyone gets 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.
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.
Personal Chronicles. This name gives the idea that your private snap story is like a personal diary, chronicling your unique experiences, thoughts, and feelings that you only want to share with a select few. It has a bit of a nostalgic and personal touch to it.
You could go for something like 'My Secret Snap World' or 'Snap Tales of Me'.
'My Secret Moments', it's simple and directly shows that it's about your private moments.
Well, how about 'Behind the Scenes' or 'Personal Glimpses'? They give a sense of privacy and exclusivity.
Well, 'Behind the Scenes' is a nice option. It gives the idea that there are things not usually seen. Another one could be 'Personal Paradise', suggesting a special and private place for you.
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.