Googling for Spock's full name, I came across the Memory Beta-Wiki
which lists his name as "S'chn T'gai Spock".
It goes on to say, "As is the case with most Vulcans, only his last name was used due to the difficulty non-Vulcans would have in pronouncing his full name, although on at least one occasion Spock revealed his full name."
Okay, now I'm looking for that at least one occasion. Was it in a TV-episode or one of the movies? Or a novel - if so which one?