I believe "Vyasa" just means "editor". Are his ancestors mentioned? Were they all "vyasa"s?
This is the text about ancestors of vyasa from Mahabharata
Vaisampayana said, "I bow unto that great Rishi who is the dispeller of darkness, and whom Satyavati bore to Parasara in the midst of an island, who is possessed of great knowledge and who is endued with great liberality of soul. The learned say that he is the origin of the Grandsire Brahma; that he is the sixth form of Narayana; that he is the foremost of Rishis; that he is endued with the puissance of Yoga; that as the only son of his parents he is an incarnate portion of Narayana; and that, born under extraordinary circumstances on an Island, he is the inexhaustible receptacle of the Vedas. In the Krita age, Narayana of great puissance and mighty energy, created him as his son. Verily, the high-souled Vyasa is unborn and ancient and is the inexhaustible receptacle of the Vedas!"
Janamejaya will recite the ancestors of Vyasa as happened in Dwapara yuga
"O best of regenerate persons, it was thou that saidst before this that the Rishi Vasishtha had a son of the name of Saktri and that Saktri had a son of the name of Parasara, and that Parasara begot a son named the Island-born Krishna endued with great ascetic merit. Thou tellest me again that Vyasa is the son of Narayana. I ask, was it in some former birth that Vyasa of immeasurable energy had sprung from Narayana? O thou of great intelligence, do tell me of that birth of Vyasa which was due to Narayana!"
Source: Santi parva