Saturn in Hebrew is Shabbatai, from the same root as Sabbath, because Saturn holds the seventh day. The planet and the rest are named for each other, and Cassiel inherits both.
The Heptameron gives him Saturday. The name is unstable in transmission even by the standards of this subject: Cassiel, Casziel, Qafziel, Kafziel and Castiel all appear in lists that are otherwise describing the same office, and later devotional and popular literature has picked up several of them independently.
Saturn's classical character governs what the tradition then says about the angel. Saturn is the outermost of the seven visible spheres, the slowest, the coldest, the planet of limit, time, endurance, mourning and solitude. Its metal is lead and its temperament is melancholic. The grimoire literature accordingly gives Saturn's angel a notably restrained character, an angel more often described as observing and permitting than as acting, which is a reading of the planet rather than a report about the angel.
The same structural problem appears here as with Jupiter. The sephirotic table assigns Binah, Saturn's sphere on the Tree, to Tzaphkiel, so one planet carries two archangels depending on which system is consulted, and the two names have nothing to do with each other. As with Michael and Raphael, the disagreement is real, old, and unresolvable, because no authority stands over both systems.