I used to write two reports. The Rehearsal report only went to production management & the company head, and included start times, end times, and any personnel notes, e.g., tardiness, absences, scheduling conflicts, personality conflicts. This document was written as evidence in case of terminations or future lawsuits. In this case I always referred to myself as my role for the sake of clarity, as the rehearsal report could very well be used by the company many years later.
The Tech Notes went to the design team and implementation leads. (TD, Wardrobe, ME, Props, etc.) This was for all of the concrete decisions and needs that evolved during the course of the rehearsal and was designed for clear communication. For Tech Notes I'd use far more colloquial phrasing, and would generally refer to myself by name or in the 1st person. This was mostly due to doing remounts. When saying "stage management did X" in the context of a remount, it becomes a bit vague as to whether you're referring to the present day or the original production.