Herdalicious - you may tell anyone you want anything you want.
I can tell you that a public entity (university, school/school district, hospital, government agency, business, church, etc.) would get the living poop sued out of them if they released the name publicly. As a contact tracer, I cannot and do not mention the name of the "case" when following up on the situation. You can only explain to someone that they may have been exposed to COVID (based on the information shared with the contact tracer by the "case"), that they are advised to self-quarantine for 14-days from the initial date of exposure, and that if they have any symptoms of COVID they should contact their physician for medical guidance. If you're interested, there is a 6-hour contact tracing training available free of charge on the Johns Hopkins University website.
By the way... that was a serious answer as well - not being a jacka$$. Just the facts man!