AIBU to expect those who test Covid positive to tell others?

The context is a choir I sing with. We all do a lateral flow test before the rehearsal, but since last Wednesday, five members have notified the secretary that they have since tested positive for Covid. All we are told is Two Altos, One Bass etc. I have asked for names but not everyone is prepared for their name to be publicised.
Personally I think there is not much point telling us numbers without names. We sit with a distance between chairs, have loads of ventilation and wear masks if moving around, so actually it is very easy to know which people have been near you.
I want the choir to be as safe a place as possible, so I think we need the information to assess our risk, but the Secretary says individuals have a right to privacy.