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.
'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.
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.
'My Secret Shenanigans'. It gives a sense of mystery and fun, like you're up to something silly but private.
'My Secret Snapshots', it gives a sense of mystery and privacy.
My Secret Moments. It gives the idea that the story contains personal and private happenings that are only for a select few to see.
Some other great names might be 'Exclusive Exposures', 'Hidden Highlights', or 'Confidential Chronicles'. These names give a sense of privacy and exclusivity which is perfect for a private story. The idea is to choose a name that reflects the personal nature of the content that will be shared in the snap private story.
Forbidden Fragments. The word 'forbidden' gives an air of secrecy, and 'fragments' can imply that the snap story is made up of different parts of your private life that are not meant for public consumption. This name makes it sound alluring and private at the same time.