You can use 'Personal Pranks Galore', 'Exclusive Eccentricities' or 'Confidential Comedy'. 'Personal Pranks Galore' is perfect if you often share pranks or funny tricks in your private story. 'Exclusive Eccentricities' shows that the things in your private story are unique and a bit out of the ordinary. 'Confidential Comedy' simply indicates that it's a place for comical content that is private.
How about 'My Mysterious Musings', 'Sneaky Snaps' or 'Covert Craziness'?
Some funny names could be 'Private Pandemonium', 'Secret Shenanigans' and 'Hidden Hijinks'. 'Private Pandemonium' gives the impression that there's a lot of chaotic and fun stuff going on in your private story that others don't get to see. 'Secret Shenanigans' implies some sort of mischievous or fun activities that are kept under wraps. 'Hidden Hijinks' also suggests that there are some exciting and comical things hidden away in your private snap story.
Private Moments Gallery. This name gives the idea that your snap story is a collection of personal and private moments that are precious to you. It has a bit of an artistic and exclusive feel to it.
How about 'Secret Silliness', 'Hidden Hilarity' or 'Private Pranks'?
Some good ones could be 'Confidential Chuckles', 'Exclusive Escapades' and 'Restricted Ridiculousness'. These names give a sense of secrecy and fun at the same time. They can make your private stories seem more interesting and unique. For example, 'Confidential Chuckles' implies that there are some really funny and private things that only a selected few can see, which is exactly what a snap private story is all about.
You can use 'The Jolly Jumbles' or 'The Wacky Wonders'.
You could use 'Secret Silliness', 'Hidden Hilarity' or 'Private Pranks'.
You could use 'Secret Scribbles' or 'Hidden Hilarities'.
'Secret Chronicles', 'Hidden Tales', 'Personal Reveries' are great creative names for private stories.
'My Secret Shenanigans'. It gives a sense of mystery and fun, like you're up to something silly but private.
You could use 'Secret Snippets', 'Personal Chronicles', or 'Private Moments'.