Name. The name Olmec means rubber people in the Aztec 's language: Nahuatl. It was the Aztec name for the people who lived in this area at the much later time of Aztec dominance. Ancient Mesoamericans, spanning from ancient Olmecs to Aztecs, extracted latex from Castilla elastica, a type of rubber tree in the area.t was the Aztec name for the people who lived in this area at the much later time of Aztec dominance. Ancient Mesoamericans, spanning from ancient Olmecs to Aztecs, extracted latex from Castilla elastica, a type of rubber tree in the area.