Star Trek

It was always my understanding that "Spock" is his first name.

In some cultures, in even old-time human cultures, each family member had a name and then there was the "family" name (like the De Medicis of Italy)

When Spock says his other name is unpronouncible, he is referring to his family name. 

(Note: Leila never asks about Spock's "last name", she says "you never told me if you had another name, Mr. Spock")

And, also...

The reason Spock is referred to as "Mr" is that all officers on the bridge are referred to as Mr, even females  (In the Wrath of Khan, Saavik is referred to as "Mr" Saavik)

I thought his name was just Spock however he did mention that he had another name but it would be hard to pronounce.

According to D.C. Fontana, in her novel "Vulcan's Glory", Spock's full name is, if memory serves, Spock, son of Sarek of the House of Surak of the noble clan Telek-sen-deen.

Put all that in Vulcan, and you have quite a mouthful.

i always just figured vulcans only had one name.