Spock (full name S'chn T'gai Spock) was a famed half-Vulcan/half-Human Starfleet officer who served the Federation in the 23rd and 24th centuries. 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.

Do Vulcans have first and last names?

Surname. A surname, family name, or last name was a name added on to the given name of an individual, often to indicate a family or clan relationship. The unpronounceable Vulcan name was described as a "first name" in TOS: "This Side of Paradise". No Vulcan family name has been given in canon.

Who came up with the name Spock?

The ancestors of the Spock family arrived in England following the Norman Conquest of 1066. The name Spock came from the Norman given name Espec.