The name of the first man to step on the Moon is Neil Armstrong. He was the commander of the Apollo 11 mission, which successfully landed on the lunar surface on July 20, 1969. Upon stepping onto the Moon, Armstrong famously declared, "That's one small step for [a] man, one giant leap for mankind," marking a monumental achievement in space exploration. His contribution to the mission and subsequent endeavors in aerospace engineering solidifies his legacy as a pivotal figure in human history.