The Mesa Bartender is a new Host that Elsie Hughes was programming to be a new bartender for Westworld. While programming she seems to call him either "Bart" or "Art". So far, he continuously misses the glass as he pours from the bottle of liquor.
It seems Elsie got the bartender's coding correct, as we see the bartender in "The Adversary" working on the Mesa Hub's rooftop pool area. He is told to stop serving drinks to Lee Sizemore.