Names to give to your Snapchat private story
You might consider 'Exclusive Snap Tales'. The word 'exclusive' makes it seem special and only for a select few (in this case, just you). Also, 'tales' gives it a bit of a story - like feel which is great for a collection of snaps. For example, if you're using it to document your travels, each snap is a part of the travel tale. So it works well for various types of content that you might want to keep private on Snapchat.
Another option is 'Secret Snap Snippets'. 'Secret' emphasizes the privacy, and'snippets' implies that it's made up of small pieces or moments, which is what snaps usually are - short moments captured in time.
Names for your private story
Some other names could be 'Exclusive Episodes', 'Private Pages', or 'Confidential Chronicles'. These names give a sense of something that is only for a select few or for your own personal records. For example, 'Confidential Chronicles' implies that it's a collection of stories that are private and perhaps a bit like a journal that you don't want everyone to see.
Can people see who's on your private story on Snapchat?
No. Snapchat keeps the list of viewers for your private story private.
Names to call your private story
Another option could be 'Intimate Narratives'. This name implies that the stories are something private and close to you, and it has a bit of a mysterious and alluring feel to it.
Fun names for your private story
Some fun names might be 'Exclusive Escapades' or 'Personal Pandemonium'. The idea is to choose a name that reflects the private and unique nature of the story. For example, 'Secret Scribbles' gives the impression of a personal journal where you jot down your thoughts and experiences that are only for you or a select few. 'My Hidden Chronicles' is also a good one as it implies a series of events or stories that are hidden away from the general public, much like a private story should be.
Names to call your private story
You could call it 'My Secret Chronicles', 'Personal Tales', or 'Hidden Moments'.
Names to call your sc private story
How about 'Personal Tales Unveiled'? It gives a sense of the private nature of the story.