The Dalai Lama was born Lhamo Thondup but according to wiki his current name is Jetsun Jamphel Ngawang Lobsang Yeshe Tenzin Gyatso which is typically shortened to Tenzin Gyatso.
Currently his name fields are Display= 14th Dalai Lama, Tenzin Gyatso; Title = The 14th Dalai Lama; First Name = Tenzin Gyatso.
I think we should leave the Display Name as is but change First Name = Lhamo Thondup and add to the AKA = Jetsun Jamphel Ngawang Lobsang Yeshe Tenzin Gyatso