Add one simple field, either to the profile or freestanding. Make it just be a text string indicating what even you are currently (this ride) participating in. Show it on the screen and in the rider list. Maybe filter the rider list, maybe that is a separate thing. Then append the string to the strava activity saved.
Perhaps it should be 2 fields. An event name and a class. Or it could just be a combination.
Even better would be a very simple way for leaders to organize and event and have an selection box to pick a current even to ride in. That way we would avoid the current confusion of screen names of ZTR (A) vs ZTR A vs. (ZTR A) activities names. And we wouldn’t have to be remembering and checking as we’re trying to get setup to go, maybe having to change our profile name and restart and hope it still works in time.