'My Exclusive Snap Album'. 'Exclusive' makes it clear that only a specific group of people are allowed to view the snaps in this private story. And 'album' gives the impression of a collection of memories or moments that are precious and private.
'My Secret Snapshots', it gives a sense of mystery and privacy.
Private Picture Parade. It has a bit of a fun and exclusive feel, as if it's a parade of pictures that only you or a few selected people can view.
You could use names like 'Hidden Highlights'. It gives the idea that there are special moments in the private story that are not for everyone to see. Another option is 'Personal Passages', which implies that it's a journey or story that is unique to you on a personal level. And 'Intimate Insights' is also a great name as it suggests that the content in the private snap story is something private and gives an insight into your life.
'My Secret Shenanigans'. It gives a sense of mystery and fun, like you're up to something silly but private.
'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.