Consider 'Snap Escapades'. The word 'escapades' gives a sense of fun and adventure, so it would be a good name if your snap story is full of exciting or interesting things. 'My Snap Chronicles' is also a good choice. It makes the snap story seem like a series of events or experiences that are being chronicled, much like a historical record but in a more modern and personal way.
You can use 'Snap Highlights'. This name indicates that the snaps in the story are the best or most interesting parts of your day or an event. Another one is 'My Snap Recap' which implies it's a summary of things you want to share through snaps.
For a snap story, 'Snapshots of Me' is a simple yet effective name. It tells people that the snaps are all about you. 'My Visual Story' is also a great option as it emphasizes that the snap story is a way of telling a story through visual means, like pictures or short videos.
You could call it 'My Daily Adventure'. It gives a sense of something exciting that happens every day in your life and is shared through the snap story. Another option is 'Moments in Time' which implies that it's a collection of special moments you've captured.
'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.
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.
You could call it 'My Secret Chronicles', 'Personal Tales', or 'Hidden Moments'.
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.
You could go with something like 'My Daily Adventures' or 'Fun Times Unfiltered'.
How about 'Personal Tales Unveiled'? It gives a sense of the private nature of the story.
'My Secret Shenanigans'. It gives a sense of mystery and fun, like you're up to something silly but private.