People do not usually use 「名」today. 「名」sounds very archaic. We listen to it only on 时代剧,like 「そなた、名は何と言う?」("What is your name", usually used by princess, prince or kings to people in lower positions ).
The movie title 「君の名は。」is originated from a famous movie of the same title, which was released in 1953 so its title is in old Japanese.