good names to call 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'.

You could call it 'My Secret Chapter', 'Personal Chronicles', or 'Hidden Tales'.

Some names might be 'The Unshared Narrative', 'Private Pages', or 'Secret Scribbles'. These names give the idea of something that is only for you or a select few to know about. For example, 'The Unshared Narrative' emphasizes that this is a story that is not meant to be spread widely, but rather kept within a particular group or just to oneself.

You could call it 'My Secret Chapter', 'Personal Chronicles', or 'Exclusive Tales'.

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'.

How about 'Personal Tales Unveiled'? It gives a sense of the private nature of the story.

You could call them 'Secret Chronicles', 'Hidden Tales', or 'Personal Sagas'.

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.