The Naiman khan defeated by Genghis Khan’s forces in 1204 was Tayang Khan.
Tayang Khan ruled the Naiman, a powerful steppe confederation west of the Mongol heartland. After Genghis Khan defeated the Kerait ruler Toghrul in 1203, Toghrul fled toward Naiman territory and was killed by a Naiman patrol. Tayang Khan then decided to confront Genghis Khan, despite opposition from some advisers.
The two armies met in 1204 in the Khangai Mountains, in the battle commonly identified as the Battle of Chakirmaut. The question’s reference to the Altai Mountains is therefore a geographic error or loose wording; the defeated Naiman leader was nevertheless Tayang Khan. His army was worn down by Mongol maneuvering and repeated attacks before the decisive fighting.
Tayang Khan was killed during the battle, while his son Kuchlug escaped and later became a significant rival of the Mongols. The defeat broke Naiman power in Mongolia and helped Genghis Khan consolidate control over the major steppe tribes.