His successor was Sonam-gyatso. He was invited to Mongolia by the famous conqueror Altan Khan, and on his arrival at the latter’s camp the Khan addressed him in Mongol by the name of Dalai lama, the Tibetan word gyatso, “ocean” being the equivalent of dalai in Mongol. Altan, knowing that the lama’s predecessor had also the word gyatso in his name, took it for a family name; and this mistake has been the origin of the name of Dalai lama since given to all the reincarnations of the Grand Lama.
In 1642 Kushi Khan conquered Tibet, and made over the sovereignty of the central portion of it to the fifth Dalai lama, Nagwang lozang-gyatso, and that of Tsang, or Ulterior Tibet, to the Grand Lama of Tashilhunpo, though he continued himself to be the de facto sovereign, appointing Sonam chuphel as Desi, or Governor, of Central, and another as administrator of Ulterior Tibet. The spiritual government remained, however, in the Dalai lama’s hands, and he conferred on Kushi Khan the title of Tandjin chos-gyi Gyalbo, "the most Catholic king."
In 1645 the Dalai lama erected the palace of Potala, Kushi Khan having his residence in the Gadan khangsar palace in Lhasa itself. Engrossed with extending and consolidating his newly acquired kingdom, he had, little by little, to transfer to the Dalai lama and the Desi most of his authority over Tibet. In 1654 Kushi Khan died, and the Desi Sonam chuphel followed him shortly to the grave. By this time so much of the temporal authority had devolved on the Dalai lama, that, from the time of the death of Kushi till his successor Dayan arrived in Lhasa in 1660—even though for a year (1658–1659) there was no Desi—the country enjoyed peace and prosperity under his rule.
During Dayan Khan’s reign, which only lasted eight years, a Mongol chief, Jaisang Teba, was Desi of Tibet, and the Desi who succeeded him was appointed by the Dalai lama himself.
The successor of Dayan was Ratna-talai Khan, but by this time the management of State affairs had entirely passed into the hands of the Grand Lama. In 1680 he appointed Sangye-gyatso Desi, and conferred on him such authority that, under the title of Governor-Treasurer (Sa-kyong-wai chyag-dso), he was in reality King of Tibet. He remodelled the Government, and introduced many useful reforms in every branch of the public service.
The Desi is commonly called "regent" (gyal-tsab), or "king"