@HP, as I understand it, no one can claim the title. Elder lamas have to recognize the heir to the title, and sometimes it takes a long while—years. The thinking is that the new incarnation will reveal him- or herself.
I believe the Dalai Lama’s stated reason for not reincarnating was that the Chinese authorities have said they will pick the next incarnation, and undoubtedly they would pick a Chinese. DL said that person wouldn’t be him, that he would not reincarnate as their choice, under their control, and that to avoid that conflict he just wouldn’t reincarnate.
I read all this years ago, so if I’ve got any if it muddled, I hope someone will set me straight.