Some great names could be 'The Ridiculous Ruminations'. This name suggests that the private stories are going to be about some really absurd thoughts or events. 'The Droll Dialogues' is also a good name as it implies that the stories are going to be full of funny conversations. 'The Amusing Anecdotes' is another option which indicates that the stories are going to be short and funny stories about different things.
You can use 'The Jolly Jumbles' or 'The Wacky Wonders'.
How about 'The Secret Silliness' or 'My Whimsical Whispers'? Another option could be 'The Hilarious Hideaway Tales'.
How about 'Secret Sillies' or 'Whimsical Whispers'? Another option could be 'Crazy Chronicles'.
How about 'My Mysterious Musings', 'Sneaky Snaps' or 'Covert Craziness'?
My Secret Moments.
My Intimate Recollections. This name is great because it emphasizes the intimacy of the stories. When you think of recollections, it's about memories, and the 'intimate' part makes it clear that these are personal and private memories that are being shared in the private story.
You could use names like 'My Secret Chronicles', 'Personal Moments', 'Exclusive Tales'.
'Secret Chronicles', 'Hidden Tales', 'Personal Reveries' are great creative names for private stories.
How about 'Unseen Narratives' or 'Cloaked Chronicles'?
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.
You could go for something like 'The Secret World of [Your Name]' or 'My Hidden Adventures'.