I've been wondering, has Spock's full name S'chn T'gai Spock ever been spoken out loud by any character?
"Out loud?" If you mean onscreen, certainly not, since it comes exclusively from the novels. If you mean, was it used in dialogue by a book character, not as far as I know. To the best of my knowledge, it's been used in only three books. Ishmael, where it originated, used it only in a computer-screen text readout. The Tears of Eridanus had Sybok introduce himself as "son of Sarek, of the family S'chn T'gai, of the Clan Hgrtcha," but Spock did not exist in that universe. And Uncertain Logic mentioned the family and clan names only in narration. So there is one instance where the family name was spoken "out loud" in a book, but not Spock's full name specifically.