Hm, no idea if this the 'actual' etymology or if this is the rationale for calling squid Teuthids - but from what I can gather, Teuthis was a Greek general in the Trojan war, who's most notable achievement and place in history comes from apparently spearing the goddess Athena in the thigh for trying to dissuade him from something or other (these ancient greeks and their histrionics! ).
Now - one could draw a logical thread from the ballistic tentacle strike of squid to that of a 'spearing' of its prey, so perhaps the teuthid designation could have been so inspired. Or perhaps the pen of the squid reminded the taxonomer of a spearhead. There was a city also called Teuthis (not clear on whether the general or the city is the namesake of the other), so perhaps there is a geographical connection to the original defining of Teuthida for squids. I think some detective work and historical context for the event of naming of the Teuthida thus is needed in addition to just the connection to place- or person-names.
So - Greek, yes. Why? Not sure. Speculate away! I bet the most round-about reasoning we can come up with is still simpler than that actual reason though.
Maybe we can all make up a just-do story about 'how the squid got its name'? I'd love to see some attempts from our learned members!
I borrowed this from Wikipedia: Leads me to believe that Teuthis is not a direct translation for squid in Greek.
The word Calamari is the plural form of the Italian word for squid, Calamaro.
Also known as Kalamari (Greek), Kalamar (Turkish), Calmar (French), Kalmari (Finnish), Calamar (Spanish), the name derives from the Late Latin word calamarium for "ink pot", after the inky fluid that squid secrete. Calamarium in turn derives from Greek kalamos (κάλαμος) meaning "reed," "tube" or "pen".
Nope, definitely not a direct translation. In general I think higher-order taxon names are often a lot more obscure than Genus - species, which often follow 'morphology - place/distribution' (Octopus vulgaris) or 'morphology - name of important person/describer' (Octopus bocki) or 'horrible corruption of various similar words from three or more languages - anatomical feature' (Octopus bimaculoides) or something like it.