Kokochu was a son of Munlik of the Khongkhotan, a man close to Temujin's family since Temujin's childhood, and he bore the title Teb Tengri, usually understood as the wholly heavenly. He was a shaman in the specific sense the steppe used: a specialist who travelled to the sky, brought back what heaven had said, and could be checked against whether it came true.
What he is remembered for is applying that authority to the succession. One strand of the tradition credits him with proclaiming that Eternal Heaven had given the earth to Temujin and with announcing the title by which the ruler would afterwards be known. The Secret History of the Mongols gives a different account of how the title was taken, and the discrepancy is itself informative about how these sources were assembled.
It went wrong when he turned the same authority against the ruling family. The Secret History has him say that heaven had shown him the rule passing sometimes to Temujin and sometimes to his brother Qasar, then seize and humiliate Qasar, then draw followers away from the youngest brother Temuge. Temuge complained, and the ruler's wife Borte warned that a man who broke the brothers would break everything. Temuge was allowed to arrange a wrestling match at which Kokochu's back was broken. The body was left in a tent that was afterwards found empty, which the account presents as heaven having taken him rather than as a miracle in his favour.