Health Department may authorize physician to write standing order prescriptions without patient name or date for treatment of STDs to be filled out and delivered to patient by nurse. Utah Code Ann. § 58-17b-620.

A health department may implement the prescription procedure under Subsection (3) for prescription drugs, other than controlled substances, for use in clinics providing: (a) sexually transmitted disease treatment; (b) fluoride treatment; or (c) travel immunization. [Subsection 3 provides that] the following prescription procedure shall be carried out…: (a) a physician writes and signs a prescription for prescription drugs, other than controlled substances, without the name and address of the patient and without the date the prescription is provided to the patient; and (b) the physician authorizes a registered nurse…to complete the prescription written … by inserting the patient's name and address, and the date the prescription is provided to the patient, in accordance with the physician's standing written orders and a written health department protocol approved by the physician and the medical director of the state Department of Health.
Utah Code Ann. § 58-17b-620(2)-(4)

It is considered unlawful conduct for a pharmacist to dispense a prescription drug “to anyone who does not have a prescription from a practitioner....”
Utah Code Ann. § 58-17b-501(10)

EPT is permissible.

Statutory authority expressly allows for anonymous STD treatment. An attorney general opinion allows for third-party prescriptions without prior physical examination. EPT, however is only allowed for the treatment of STDs and cases recognized by official opinions. Outside these cases, it is unlawful for a pharmacist to dispense drugs for anyone who does not have a prescription.