In this story, it seems Sanae has not been told of the true identity of the god, or rather gods, of her shrine yet. According to Suwako and Kanako's ancient scheme, the shrine is supposedly dedicated to a god of Moriya, while Kanako is kept secret, which is probably why she has not heard the name "Yasaka" before.
Also, Kanako is probably not simply acting cold against the old priest, but is rather trying to act divine, perhaps to give him some last comfort in his faith. And it is clearly an act, as her later reaction reveals. She seems to have been a lot more fond of the priest than she lets on.
I didn't think of her response as acting cold at all. Rather, it seemed to fit the style of the manga on the whole. She was expressing her grief at the short length of human lives, just in a very theatric way.
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