Family Secrets, Family Keepsakes, or Family Memories could be good names.
You can name it 'My Treasured Moments', 'Personal Photo Vault', 'Private Picture Gallery'.
You could call them 'Secret Chronicles', 'Hidden Tales', or 'Personal Sagas'.
One possible name is 'Gentle Gay Secrets'. It has a soft and private connotation. Another good name could be 'Gay Secluded Stories' which implies that these are stories that are set apart, private. 'The Quiet Gay Tales' is also a nice name as it gives the feeling of something that is not out in the open and is for a more private audience.
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'.
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'.
Well, how about 'My Exclusive Escapade' or 'The Privy Plot'? These names can make your private story seem more interesting and special. They give the idea that it's something that's only for a particular group or just for you. Like 'The Privy Plot', it makes it sound like there's a secret plan or story that only you are privy to.
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.