What is the medical term meaning specialist in the diagnosis and treatment of STDs?

Answer 1

"Venerologist" is a rather old-fashioned term for an STD specialist. In reality, health care providers in many different specialties can diagnose and treat STDs (see related question).
Most general practitioners, internal medicine doctors, and infectious disease doctors work with STDs.
They're usually just normal doctors

Answer 2

There is not a specific STD doctor; you can see your primary care provider, adult medicine, general practitioner, pediatrician, family doctor, OB-GYN, or urologist. Infectious disease specialists are sometimes consulted for cases with resistant strains, or in the case of penicillin allergy in a patient with syphilis.

You can see your primary care provider, gynecologist, urgent care clinician, or local public health department. Any doctor can test for STDs, although some have more experience and training in this area. If you're not sure where to go, consider your local department of health or family planning agency.
You can see your regular physician or visit a walk in clinic, you don't have to visit a specialist for VD.