Count Dracula, Mrs. Dracula, vampires, blood whisperers, etc. These are some of the nicknames given to these professionals who draw blood at medical offices, laboratories and hospitals.

The root term [-phleb-] derives from the Greek  [φλέβα] (phleba) meaning "vein", and the suffix [-otomist] has two components. First [-otom-], from the Greek [τομή] (tomi) meaning "to cut" or "to open" and [-ist] from the Latin [-ista] meaning "he/she who makes or does".  The medical term [phlebotomist] means "he/she who opens veins", a perfect description for these professionals.

For centuries a standard practice in medicine was to "bleed" a patient, by opening a vein under controlled conditions and letting some blood flow. The practice was known as "bloodletting" or phlebotomy, not in use today.  

The image shows a phlebotomist at work using the Vacutainer system for drawing blood

Image by Richardelainechambers (Own work) [Public domain], via Wikimedia Commons