As a biological name for humans, Homo sapiens — literally "wise human", although I sometimes like to translate it as "wise guy", with every ounce of sarcasm I can muster — was first used by Carl Linnaeus in his Systema Naturae of 1735, although I'm not sure if the name appeared in the first printing or was introduced in a later edition (of which there were many). Incidentally, Linnaeus was also the first naturalist to classify us with the other primates rather than separately (or apart from nature entirely).

Binomial nomenclature had been around as a concept for a couple hundred years before Linnaeus, but he was the first to really systematize it into the classification scheme we still use today.