Elite Gym Annex. 'Elite' implies a high - quality, private - like experience, and 'Annex' makes it seem like a special, private part of a larger concept.
Here are a few more ideas. 'My Gym Privacies' makes it clear that it's about the private experiences at the gym. 'Gym Solitude Stories' can be used if you want to convey that these are stories from the quiet or personal moments at the gym. 'Inner Gym Journeys' is also a good one as it gives the sense of the personal growth and experiences that happen within the gym environment, which are private to the individual.
Sweat and Success Tales. It implies that the content of the private story will be about the hard work in the gym and the achievements that come from it, which is very relevant for a gym - related private story.
Well, there are quite a few options. For example, 'Fitness Secrecy'. This name suggests that the story is about something private related to fitness, which is perfect for a gym private story. 'Gym Confidential' is also a great choice. It has a mysterious and private connotation, making it suitable for a private story about the gym. And 'Personal Gym Chronicles' is a name that makes it seem like a collection of personal stories from the gym.
Good names could include 'Gym Hideaways'. It gives the impression of a private place or experience in the gym. 'Personal Gym Escapades' is another great one. It implies that these are personal adventures in the gym that are private. 'Gym Confidences' is also suitable as it gives the sense of sharing private things or feelings related to the gym on the Instagram story.