The moment
The Mongol ruler Altan Khan invited the Gelug leader Sönam Gyatso to meet him in the Kokonor region and gave him the title Dalai Lama, 'ocean' teacher. Altan made Gelug Buddhism the religion of his people, the title was extended back to Sönam Gyatso's two predecessors so that he counts as the third, and the next Dalai Lama was found among Altan's own descendants.
People: Altan Khan, Sönam Gyatso, 3rd Dalai Lama