Σαδδουκαῖος (saddoukaios, G4523) from Σαδώκ (sadōk, G4524), so it’s a claim to Zadok’s lineage.
Insiders, self-justifiers
The Sadducees (Hebrew: צְדוּקִים, Ṣəḏūqīm, literally “Zadokites") were a sect active during the Second Temple period. The plural noun form is essentially a political/sectarian label, not a biblical one. Geiger's theory deriving the name of the Sadducean party from the biblical appellative "Zadok" is considered the most probable, and the name occurs ten times in Ezekiel, Ezra, and Nehemiah — but as the proper name, (sons of…) Zadok, not as a collective.
The Sadducean elite likely adopted the language of Zadokite descent as a political fiction, legitimizing their Herodian-era priesthood through a rhetorical link to the ancient priestly dynasty rather than through verifiable genealogy. Josephus records no fewer than twenty-eight high priests between Herod and the fall of the Temple — impossible if hereditary descent still governed the office. The Sadducean elite were part of this revolving door of politically installed priests.
“The Sadducees... have only the rich on their side, but no one else; yet they are able to persuade none but the rich, and have not the people following them.” (Antiquities 13.10.6)
Contrasted with the Essenes,
“They shall be ruled by the huios ho Zadok, the priests who keep the covenant, and by the multitude of the men of their covenant who hold fast to the covenant.” (1QS 5.1–2)