Nevermind, TIL apparently there is a special authority in China with the job to follow exactly the rituals of old in selecting reincarnations.Parody aside, next Dalai Lama would be chosen by the Buddhist association, as those are the ones that technically have the right. And they chose the Panchen Lama as well.
Since things are modernized now, the new dalai Lama will only be a religious figure and not someone granted powers nor state privileges by birth.
There is another method with a golden urn, but it is associated with the dark ages in China, although technically applicable, I don't think that is how the next Dalai Lama will be selected in a modern day society.
I didn't think they would do stuff like that given how secular the government is.