Names like 'My Private Panorama', 'Hidden Histories', 'Confined Chronicles' would work well. 'My Private Panorama' gives the feeling of a complete view of something that is only yours. 'Hidden Histories' implies stories from the past that are not known to many. 'Confined Chronicles' suggests that these are stories that are restricted to a certain group or just to you.
How about 'Solemn Stories', 'Individual Insights', 'Private Perspectives'? 'Solemn Stories' can be used if your private story has a serious or important tone. 'Individual Insights' emphasizes that it's your own thoughts and experiences in the story. 'Private Perspectives' gives the idea that it's a view of things that only you or a few people get to see.
You might consider 'Veiled Vignettes'. Vignettes are short, descriptive scenes or stories, and the 'veiled' part makes it private. 'Privy Perspectives' is also a good choice as it implies a perspective that is private or known only to a few. 'Reserved Recounts' gives the sense that these are stories that are reserved or held back, which is perfect for a private story.
Other possible names are 'Personal Parable', 'Secret Script', 'Intrinsic Story'. 'Personal Parable' can be used if the private story has some sort of moral or lesson within it that is personal to the teller. 'Secret Script' makes it seem like there is a written or unwritten script of a story that is secret. 'Intrinsic Story' gives the feeling that the story is an essential and private part of someone's life or experience.
You could call it 'My Secret Chapter', 'Personal Chronicle', or 'Exclusive Narrative'.
Sure. Try 'Private Pump Palace'. The word 'private' is right there in the name, and 'pump' and 'palace' give it a fun and exclusive feel.
Forbidden Views. It suggests that the content in the snap story is not for everyone to see, like something exclusive and private.
Sure. 'My Own Storybook', 'Solo Stories', 'Private Passages'.
There are some interesting names you can consider. 'Workout Wonderland' gives the feeling of a special place for your workout experiences. 'Fitness Fantasyland' implies that it's a place where all your fitness dreams and efforts are stored. Also, 'Muscle Memory Lane' can be a great name as it has a connection to the progress and experiences related to building muscle during workouts.