Spock's full name is S'chn T'gai Spock. From memory beta, Spock's full name was revealed in TOS novel: Ishmael. In TOS episode: "This Side of Paradise", Spock said that his full name was unpronounceable to Humans. But, it is now easy to recall that S'chn T'gai Spock was a famed half-Vulcan/half-Human Starfleet officer who served the Federation in the 23rd and 24th centuries.

Specifically, Ishmael is a novel by Barbara Hambly, set in the Star Trek fictional universe. Following the plot and story line in the novel, we find personnel record with Spock's full name as S'chn T'gai Spock and his father as S'chn T'gai Sarek. Spock's family name has never been revealed on film or TV screen.

Currently, it is held that Spock's full name is supposedly pronounced something like "Sa-chin Ta-guy Spock."

More Info: en.wikipedia.org