The question is not querying the verb. We fish today for sport and/or for food, the kitchen being the only reason for fishing historically. Undoubtedly the verb 'to fish' is derived from the word used as a noun. The word can be traced back to Proto-Indo-European peisk but undoubtedly existed thousands of years before this. Indeed it is quite likely this was among the earliest words ever used by humans.
Here we are interested in the etymology of the names of the individual species of fish. It is true to say we eat far less fish today than was ever eaten historically. Until recently salmon was an expensive and highly prized fish, although farming has not only reduced the price but made it available to all. This is nothing new, for in medieval times the fish was so plentiful legislation was passed prohibiting any lord of the manor from providing it to his charges more than three times in a single week.
Of course before they reach the table they have to be caught. Not every fish is the same, size, habitat, quality of the meat, all are taken into consideration and have different names to identify them to the angler and as a pointer to the cook, for not all fish are prepared the same way.
Some fish names are quite obvious. For example the angelfish is named for its apparent wings; the catfish for the whisker-like feelers which sense its surroundings in the murky waters in which it lives; while in the case of the bass, its name can be traced back through Proto-Germanic bars 'sharp' to Proto-Indo-European bhors 'bristle', both of which refer to the spines of the dorsal fins; and the stingray really does have barb and a 'sting in the tail'. These spines are even more pronounced in the perch, although that name comes from its stripes and is seen in Sanskrit prsnih 'variegated' and ultimately Proto-Indo-European perk 'speckled, spotted'.
The bream can be traced to Proto-Germanic brehwan 'to shine, glitter, sparkle' and referring to the scales, and earlier still to Proto-Indo-European bherek similarly meaning 'gleam, flash'. When it comes to the conger eel, the addition of 'eel' is unneccessary for Latin conger already describes 'the sea eel'. Further back in the language tree to the original Proto-Indo-European geng referring to the shape of the fish as 'the rounded object'. Smelt is a Dutch word describing 'the sand eel'.
The dace is a small freshwater fish with a name appropriate to its movements. This comes from Old French darz meaning 'to dart'. Although both tuna and tunny bear no resemblance to the humble dace, the name means the same 'to dart' but comes from Greek thynnos and/or Latin thunnus.
A flounder is a flatfish which is traceable back to at least the early Greek platys which does indeed confirm it as 'flat, broad', the same word also gave a name to the flat food fish, the plaice. A more recent naming of a flatfish is that of the sole, it is likened to the sole of a sandal and can only be said to refer to it as 'a flatfish'.
The gar is identified by its long snout, it being named from Old High German ger or earlier Proto-Indo-European ghaiso meaning 'stick' or 'spear'. Similarly the pike is known for its long pointed jaw, it was also the name of a weapon, and the swordfish is named for its many-teethed long jaw.
A hake is still a popular food fish, although rarely seen whole on the fishmonger's slab. It's name is derived from the hooked shape of its jaw, Old English haka and Old Norse haki mean 'hook'. The lamprey, once a prized foodsource, was named by the French and derived from Latin lambere petra literally 'lick rock' for the creature's habit of attaching itself to any manor of things by its mouth.
It is difficult to see if the anchovy is from Greek aphye 'small fish' or the alternative Basque anchu 'dried fish'. Today most often known as the salmon, from Old French salmun meaning 'leaper', still referred to as the lox in North America from Proto-Indo-European lax via Yiddish laks and meaning simply 'fish'.
The guppy, the most common occupant of tropical aquaria, was unknown in Europe until a Trinidadian clergyman brought a dried specimen to the British Museum in 1866. In 1925 the fish was named after the Rev R.J.L.Guppy.
The coelacanth is one of the oldest species known and yet it has one of the most recent names. It was named when thought of as extinct, discovered as a fossil and named from Proto-Indo-European kel akantha and describing 'the hollow spine'. These were the extended fin rays which the fish uses as legs, although this is not the species which first walked from the sea to the land as once claimed.
A dory is a name given to a flat-bottomed boat of Central America, itself named from the fish with a very broad base to its body. The fish gets its name from de aurare 'to gild' and a reference to its colouring. The gudgeon comes from Old French gojan, meaning 'small fish' and also the beginnings of the small strips of food in modern culinary parlance known as 'goujons'.
Halibut said to be from hali butte 'the holy flatfish' as it was eaten on holy days. Mackerel is thought to be from Old French maquerel, also used as a 'pimp, procurer' and probably some unknown reference to its reproductive habits - medieval folk had some quite eccentric ideas of animal reproduction.
Some names have been explained through some highly suspect and creative etymology. Examples incliude the dogfish, said to be named for hunting in packs. Sardines were said to have been named by the Greeks as they obtained their supplies from Sardinia. A squid is claimed to be a variant of 'squirt' for its defensive squirting of ink when endangered. The poor tench is said to be derived from Old English stenc or 'stench', and indeed the fish does have a rather unpleasant aroma.
The name of the clam can be traced back to Old High German klamm 'cramp, constriction' and thus describing what the clam is most famous for, closing tightly, although ironically the name of the bivalve is now used to describe such a state. Similarly today puny individuals are known as shrimps, while the name comes from a Germanic skrimpe quite literally 'thin cattle'.
From Greek konkhylion and meaning 'the little shellfish' comes the name of the cockle. Crabs can be traced through Old Norse krabbi 'crab', to Low German krabben 'to scratch or claw', to the Proto-Indo-European base of gerbh 'the scratch or carve', clearly named for its most distinctive feature, the claw. The crayfish, brought to English from the Old French crevice and having the suffix mistakenly pronounced as 'fish', can be traced through a Germanic word alsmot certainly with identical origins to the crab. Similarly the cuttlefish has never been described as a 'fish' until quite recently.
The name comes through Middle Low German kudel for 'container, pocket'. With a name meaning 'little mouse' , the mussel was seen as resembling the tiny rodent in both size and shape. Few will fail to see the octopus being named for being 'eight footed'. That the oyster has been a valued food source since mankind's days as a hunter gatherer is attested by the huge numbers of shells found with evidence of being opened with a stone tool. The name can be traced back to Proto-Indo-European ost meaning 'bone', later seen as Greek ostrakon or 'hard shell'.
The winkle is a shortened form of periwinkle, itself a description of its spiral shell in Latin peri 'thoroughly' and vincire 'bind, fetter'. Similarly the whelk's spiral shell comes from Proto-Germanic weluka, itself from Proto-Indo-European wel 'to turn, revolve'.
Of course shellfish are not exactly 'fish' in any sense, yet cannot be omitted. Noname is stranger than the barnacle, which was used for the species of goose well before the invertebrate. However the name of the goose is derived from Breton, a Celtic language of northern France, bernik which meant simply 'shellfish'. This linked the two as popular folklore of the day stated how the bird, which winters in Europe but breeds north of the Arctic Circle in the short summer, produced these eggs which were clearly related to the goose because of the feathery stalks being so similar to goose down. Hence it was thought that barnacle geese hatched from the barnacle shell.