There are 4 main schools of Vajrayana Buddhism: Nyingma, Kagyu, Sakya and Gelug, and the Dalai Lama is head of just one of them - Gelug. They have independent teaching transmissions and succession lines. There's common misconception about Dalai Lama being a kind of a "pope" for Buddhism at all, or for the Diamond way (that means Vajrayana) Buddhism in particular, which is simply not true.

Having said that, it is of course unfortunate that the issue with two candidates, one of them "manufactured" by the PRC regime, is on the horizon and most likely will happen. Please note this already happened for the Kagyu lineage, where two Karmapa candidates emerged in 90s; interesting that after few decades the Chinese one admitted recently he's not the real one.