Then, to throw a monkey wrench in this whole thing, how do alien minds see their ships? .
Linguistic xenology is a facinating subject.
To make matters more interesting, each and every race may have a different mindset in regard with semiotic issues.
I won't dare toutch it for I never created a race nor played a "deep character" Alien PC.
Even on this planet, different cultures have different approaches within the same sphere of activity using the same Tools, yet end up often (not always) with similar names.
In the example you give, Destroyer was initialy Torpedo Boat Destroyer. Destroyer stuck as a sexy name and all those sub-type naming to get glamour by association. So ASW Destroyer would literally mean "destroyer of anti-submarine weapons" but refer to a ASW ship larger than a Frigate and a) smaller than a Cruiser (about everywhere), or b) not filling the function of a Cruiser (Some USN ships), while the MN will use Contre-Torpilleur until 1951, then Destroyer-Escorteur until 54 then Escorteur d'Escadre, a strictly functionnal definition since.
Nobody dies for a paycheck, so beside size and function, esprit de corp and morale building come to play. Corvette was re-introduced as "Coastal Escort Vessel -Whale Catcher Type-" was not dignified enough and Sloop would be a missnomer given building standard and characteristic (see Kingfisher or Pelican classes). So recalling a glorious tradition, Corvette it was to be. Frigate was re-introduced later as "twin screw Corvette" was not inspiring enough, while larger than Corvette but remaining a cheapo alternative to Escort Sloop. BTW, calling Corvette: Coastal Escort or Patrol Sloop (a costal escort designation) would be bad for the moral of crew you knew would serve high sea as it would convey to them: you get the wrong hardware.
If you mounted torpedo (shade of W&L lawering) you were Destroyer but if to slow/small for Fleet: Destroyer-Escort (functionnal).
As to the Alien mindset: would an Aslan ever go to war on a ship named Begonia, Pink or Pansy within the type Mininal Budget Class? (the corvette were autorized as Costal Escort because HP thought that high sea would be too expensive, designer tricked in range and seaworthiness)
have fun
Selandia