The professional wrestler from the United States in Street Fighter III is Alex. He is an American fighter from New York who became the main protagonist of Street Fighter III: New Generation, debuting in 1997.
Alex’s fighting style is built around professional-wrestling techniques, including throws, grapples, slams, and powerful close-range attacks. His story begins after his mentor Tom is injured by Gill, leader of the secretive Illuminati. Alex enters the tournament to confront Gill and avenge Tom, giving the new game a personal protagonist distinct from the established Japanese martial artist Ryu.
Hugo is the most likely mix-up because he is also a professional wrestler and appears in Street Fighter III. The distinction is nationality: Hugo is associated with France, while Alex is American. Zangief is another famous Street Fighter wrestler, but he is Russian and was introduced before Street Fighter III. Sodom is a Japanese fighter associated with weapons and a fascination with American culture, not the requested wrestler.