The name Ἑκάτη (Hekátē) is so often claimed to mean 'far(-darter)' presumably based on the feminine form of ἕκατος 'far' (hékatos) but I find myself starting to question this because this title really doesn't get to the heart of her fundamental nature. It's merely the obscure being explained with the obscure. It begs the question: Why 'far-darter'? And this leads to long tales about her Artemesian arrows which only beg further questions about how all these metaphors and concepts were mashed together like this in the first place.
One thing is certain though. Where religious beliefs are involved, we must expect poetic creativity to have superceded literal reality. Any religious etymologies will unavoidably be quite meaningful, artful and multilayered. They may even transcend individual cultures and languages. A conservative approach remains important but we can't be stunted either.
Other available wordpuns shaping her name could be:
- ἕξ 'six' (hex) and ἕκτος 'sixth' (héktos)
- ἑκατόν 'hundred' (hekatón)
- ἑκατόμβα 'hecatomb, sacrifice of 100 oxen' (hekatómba)
The Piacenza Liver and the contents of TLE 131 (Laris Pulena's sarcophagus) show that Catha sits beside the lord of the underworld Pacha (aka Bacchus, Fufluns) as consort. As such the pair are equivalent to the Greek xenologisms Aita and Phersipnai (Hades and Persephone). So Catha is a goddess of earthly abundance and associated with the underworld, much like Hecate (as well as like Egyptian Isis). The similarity in name between Catha and Hecate only makes me ponder further about an unexplored link.
 Popular Etruscanists like Larissa Bonfante, Jean-René Janot and Nancy de Grummond all continue to misinform us that Catha was a sun goddess based only on contrived comparisons like Martianus Capella's obscure philosophical poetry of 400 AD and Dioscerides' equation of the Etruscan floral term *cauθa 'chamomile' with a Latin idiom 'eye of the sun'; see De Grummond/Simon, The religion of the Etruscans (2006), p.11 and Chapin, Charis: Essays in honor of Sara A. Immerwahr (2004), p.361 . This is pretentious erudition which deceitfully avoids examining Etruscan material in perverse favour of secondhand Roman sources which aren't even of the period in question.