Therin of Andor wrote:
If I recall, "This Side of Paradise" suggests that Leila Kalomi is aware of Spock's full name, but it's never been revealed canonically.
Ian, that's close, but not quite accurate. Near the end of the episode, Leila says, "You never told me if you had another name, Mr. Spock," to which Spock replies (somewhat wryly, I would argue), "You couldn't pronounce it."
I know that some fans take this exchange to be an indication that Spock has "another name," and most seem to infer that it means that he has another given name. For me, this never quite rang true. Leila and Spock could be speaking about a Vulcan equivalent for his name, perhaps in an ancient tongue, or perhaps they are talking about a family name, or perhaps even some other name he might have had in his infancy or youth, as part of some Vulcan ritual of which Ms. Kalomi is aware but that the audience is not. Also, Spock's response might not
indicate that he even has "another name," if he was, as I suggested, answering wryly.