Every time I go in for a screen they go thru the standard disclosures. One of them is that if you are positive for anything that you can voluntarily give them the names and phone numbers of anyone you’ve had sex within a set period. The clinic will contact them without disclosing your name.
In Georgia they are required to report to the state positive reports of HIV, syphilis, chlamydia, gonorrhea, Hep A-E, and a bunch of other stuff.
(On a side note.... not really surprising but the clinic I go to has suspended all STI screens for now because of social distancing requirements.)