Canon has established that a Klingon's full name includes a patronymic/house designator, such as "Worf, Son of Mogh." (Although since he was adopted, his full legal name should be Worf Rozhenko.) I sometimes wonder if "Sarek, child of Skon, child of Solkar" is a translation of the full Vulcan family name.
This makes sense. Even here on Earth we have names similar to this. Katie O'Claire is literally Katie from the town of Claire (iirc), and the Mc or Mac in names literally means "Son of", so Ronald McDonald is Ronald, son of Donald.