In "canon" (live-action and animated television series and films), Spock's first name is never given, but he tells Leila Kalomi that she "wouldn't be able to pronounce it." Perhaps relatedly, his mother Amanda mentions that her "Vulcan name" (maybe family name?) is only pronounceable "after a fashion."
In official, non-canon novels, Spock's "clan name" is given as S'chn T'gai, with his Starfleet service record as SPOCK, S'chn T'gai in the novel Ishmael.
In convention appearances, he has been called "Harold" as a joke by Jane Wyatt and "Xtmprszntwlfd" by D.C. Fontana. The latter name has shown up in some unlicensed works, such as the USS Enterprise Officer's Manual.