I think there might be a disconnect here. Anonymous and confidential are not the same thing. From stdexpress.com:

Private, not anonymous, STD testing
STD Test Express provides private, not anonymous, STD testing. This means that your name and other identifying information will be linked to your test results. Your results are part of a medical record and are protected by state and federal privacy laws. We are committed to protecting your privacy and will never share your information unless required or permitted by law as described in our Privacy Policy and Notice of Privacy Practices.

Positive results and public health agencies
STD Test Express and Analyte Physicians Group ("APG") comply with all state and federal laws that require doctors, health care facilities and diagnostic laboratories to report laboratory-confirmed cases of HIV and certain STDs to public health agencies. The information we are required to share may include your name, age and the condition for which you tested positive.