Mario used the name Jumpman in his first appearance in the 1981 arcade game Donkey Kong.
In Donkey Kong, Jumpman is a carpenter who must climb platforms and avoid obstacles while trying to rescue Pauline from the giant ape. The character was not yet presented with the full Mario identity that became familiar through later Nintendo games.
Nintendo later renamed Jumpman Mario, reportedly in connection with Nintendo of America's landlord, Mario Segale. The character's occupation also shifted: in Mario Bros., he and Luigi were presented as plumbers dealing with creatures in underground pipes.
The 1981 game is therefore important both as the debut of Mario and as the first major appearance of Donkey Kong. Pauline also predates Princess Peach, although the two characters are separate figures. Jumpman is the canonical name used for Mario in the original game's story and promotional material.