"shaming" is a bad idea, as middo noted.
"Naming and shaming" would never fly in the US, where technically we have health information privacy protection laws. For example, I was informed via email that my minor daughter was exposed to someone who tested positive for the virus, but they wouldn't reveal who had it. Since she barely goes anywhere, and the facility where it happened was "shut down for cleaning" on the same day, it wasn't hard to figure out at least where she was exposed, but we have no idea exactly who it was that turned out to have the virus. We were told, though, that she was in the same space as the person for an extended time and therefore she needed to quarantine for 14 days. Fun times!
South Korea actually used mobile phones to inform people of their exposures, I heard. For example, if the person in front of you in the check out line of the grocery store tested positive that week and you used your credit card at the chip scanner right after them, then they would send you a message via your phone to go get tested. Seemed to work well, but the privacy laws people are having a fit over it. This is what I heard, anyway. Can only wish I was there and not locked up here.