As I recall, Chief's name was a result of a conditional vision - Y&B saw two possible courses ahead of her:
A) Back Thac0 as the next chief. He would be a truly good chief, but the clan would self destruct in civil war because too many goblins would back the previous chief's son.
B) Back the previous chief's son as the next chief. He would be a poor chief, letting the clan lapse into weakness and obscurity, but the clan would unite behind him and stay whole and intact.

She saw this when she was naming the newly born son of the old chief, and named him 'Chief' as a way of making her choice between these two options and giving it the best possible chance of sticking.