What do you call a person who makes cocktails drinks?

A person who makes cocktails can be called a mixologist. This is a specialist term however and most people who work behind bars are simply called bartenders.

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A mixologist is a person who's skilled in making mixed drinks or cocktail drinks, it is also a slang term for a refined and in depth study of the art and craft of mixing. There are lots of known mixologist I know that came from different cocktail bars in the world, such as 1. Colin Field, Hemingway Bar, Ritz, Paris, France 2. Aristotelis Papadopoulos, Banquet, Thessaloniki, Greece 3. Salvatore Calabrese, Salvatore at Fifty, 50 St James, London, UK 4. Dario Doimo, Kahunaville at Treasure Island, Las Vegas, USA 5. Suraj Gurung, HK, Stockton.