The Gym Journeys. It emphasizes that each time at the gym is like a journey, and these are private accounts of those journeys. For example, you can write about how you overcame difficulties during a particular workout session or how you achieved a new personal best. All these are part of your unique gym journey that you may want to keep private.
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.