I checked all my sources, and there seems to be no consensus on the etymology of Tartatos (the abysmal region below
Hades where the Titans were confined).
One thought of mine is the following: the ancient Greek verb "tartarizo," meaning "to shiver of cold" (which survives in contemporary Greek as "tourtourizo") if very likely an *onomatopoeia* describing the sensation of shivering from cold.
However it is unclear to me if "tartarizo" gave its name to "Tartaros" or vv.