First, in Tlingit they’re called, in order: tʼá /tʼá/, g̱aat /qaːt/, lʼook /ɬʼuːk/ (cognate with Proto-Athabaskan *ɬuːqʼə ‘fish’, e.g. Denaʼina ɬiqʼa, Tsuutʼina ɬúkʼá, Navajo ɬóːʔ), téelʼ /tʰíːɬʼ/, and cháasʼ /tʃʰáːsʼ/. The generic term for ‘fish’ which by default refers to any kind of salmon is x̱áat /χáːt/.
The scientific names all come from Russian, and were originally given by Johann Julius Walbaum during his time in the Russian Far East. The name O. tshawytscha is from Russian чавы́ча /tɕaˈvɨtɕa/ which is itself from Itelʼmen čevičev. O. nerka is in Russian не́рка /ˈnʲerka/, but in Siberian dialects ня́рка /ˈnʲarka/, and which appears to be from Proto-Samoyedic *nʸʌrkə, compare Nganasan nʸorə. O. kisutch is Russian ки́жуч /ˈkʲiʐutɕ/ but in Siberian dialects ки́зуч /ˈkʲizutɕ/, coming from Itelʼmen kizuez; the dialectal form is the source of the scientific name. O. keta is particularly interesting: in Russian it is ке́та /ˈkʲeta/ but this is again not native; rather, the source is probably Evenki keːta ‘O. keta’ or perhaps Even qæta ‘dead salmon after spawning’ (unrelatedly, Tlingit also has xein /xeːn/ ‘spawned-out salmon’ < Pre-Tlingit *xayn, cognate with Eyak xaːnih; also cf. PA *xʸaːn ‘old age’, cognate with Tlingit shaan /ʃaːn/ ‘old, elderly’ < Pre-Tlingit *šaʻn) both of which are themselves probably from Chukchi-Koryak, e.g. Chukchi qetaqet ‘O. keta’. The Russian for O. gorbuscha is simply горбу́ша /gorˈbuʂa/ derived from горб /gorb/ ‘hump’ and describing the pronounced hump that develops on the backs of males during spawning.
The English names are a bit more confusing. All five species occur along the Northwest Coast (NWC) of North America down as far south as the Columbia River and some as far south as San Francisco Bay and the Sacramento River (e.g. O. keta). They also all occur on the Alaskan coast as far north as the Bering Sea, and some as far as the Arctic Ocean (e.g. O. gorbuscha and O. keta to the Lena and Mackenzie Rivers). Because English speaking colonists met with the salmon at different times and different locations, a variety of names have proliferated for them. I will try to sort them out a bit here, but the majority of my experience is in Alaska and so my knowledge about name distribution patterns is only tentative for the southern NWC. Fortunately it is Alaska that most people know little about, and I’m sure others can work out the geographic distribution down where the populations are greater and there are more people inclined to investigate.
In Southcentral Alaska, and typically throughout most of mainland Alaska, the five species are most often called: O. tshawytscha ‘king’, O. nerka ‘red’, O. kisutch ‘silver’, O. keta ‘dog’, and O. gorbuscha ‘pink’. These are all relatively transparent names. ‘King’ is obviously because it is the biggest and most prized, ‘red’ is from both the prominent red color of the skin during spawning as well as the darker orange-red color of the flesh, ‘silver’ is from the bright color of the skin, ‘dog’ comes from the pronounced teeth on males which are reminiscent of the canine teeth of dogs, and ‘pink’ is from the pale pink or pink-orange color of the flesh. This group of names can be loosely called the “color names” for the fish, and use of the full set is characteristic of southcentral Alaskans as well as many (most?) people of interior and southwestern Alaska. I can’t really comment on use in the Arctic since I have little experience up there, but I expect that white people would use the same names as found in e.g. Anchorage and Fairbanks.
In Southeast Alaska O. nerka is almost always ‘sockeye’ instead, which derives from a reanalysis of the loan /ˈsʌkai̯/ (Goode 1887 Amer. Fishes: “‘Suk-kegh’, ‘Saw-quai’, or ‘Suck-eye’”) that comes from Halkomelem sθə́kəy̓. This term is found along the coast down to Oregon. Although the term ‘kokanee’ is current in the southern NWC for landlocked specimens, I have not heard it used in Alaska but then again I have not done much fishing in the interior. The term ‘sockeye’ is not uncommon elsewhere in Alaska, but sport fishermen in southcentral Alaska seem to use ‘red salmon’ more often. The species name is never used in English, except perhaps among biologists who are strange people anyway.
Also in Southeast Alaska O. kisutch is referred to as ‘coho’, a term with an uncertain etymology. The OED2 gives a citation from the British Colonist (Victoria) in 1859: “the genus known by the Indian name of coocouse”, and from the Mainland Guardian (New Westminster) in 1869: “The second of salmon in class is the Cohose”, so presumably there is some Salishan or possibly Wakashan, Chimakuan, or Chinookan language from whence this name came. As with ‘sockeye’, the term ‘coho’ is prevalent from Southeast Alaska down the coast to Oregon. This fish also serves as a major crest of the Tlingit Lʼuknax̱.ádi /ɬʼuknaχʔáti/ clan, often called the ‘Coho People’ or ‘Coho Clan’ in English. They are named after a stream south of Klawock which is called Lʼuknáx̱ /ɬʼuknáχ/, itself named after the fish. The Tlingit name of Deep Bay is Lʼugunáx̱ /ɬʼukunáχ/ which is probably the same name. Use of ‘coho’ is in my experience characteristically southeastern, contrasting with the rest of Alaska where ‘silver’ is much more common.
O. keta is often known as ‘chum’ which comes from Chinook Jargon tsəm or čəm meaning ‘mark, spot’. It is more commonly known also as ‘dog salmon’ in Southeast Alaska, but this name is also common in the rest of Alaska as well. I don’t know if ‘dog salmon’ is common along the southern NWC or not. The ‘Dog Salmon Clan’ of the Tlingit is named after this fish, called in Tlingit Lʼeeneidí /ɬʼiːneːtí/ or Lʼeineidí /ɬʼeːneːtí/, derived from a stream called Téelʼ Héeni /tʰíːɬʼ híːni/ ‘dog salmon stream’ thus Teelʼheeneidí /tʰiːɬʼhiːneːtí/ ‘dog salmon stream people’. The salmon marketing industry has the inane name ‘Silverbrite™©®’ used to market O. keta as a cheaper alternative to O. kisutch; I have never heard the name used seriously, only derisively in reference to marketing. It obviously conflicts with the name ‘silver’ for O. kisutch, and hence would never be adopted where ‘silver’ is used. Presumably ‘chum’ and ‘dog’ are just not pleasant enough for the delicate ears of North Americans outside of its range. Rumour has it that some people refer to this fish as ‘keta’ after the scientific name, but I’ve never heard of this before and I suspect that it is again restricted to those crazy biologists.
O. gorbuscha is often known as ‘humpy’ which is widespread in Alaska, with no particular geographic emphasis, although ‘pink’ is the common alternative in southcentral Alaska (but cf. Humpy’s in Anchorage, an excellent bar/pub downtown). This name is essentially the same as in Russian, though it is probably not a calque into English but rather an independent invention from the very obvious dorsal hump of spawning males. It is not generally called ‘humpback’ since this conflicts with the humpback whale, Megaptera novaeangliae (Borowski 1781), which is more often just called ‘humpback’ in casual speech rather than ‘humpback whale’. I’ve never heard the species name used in English, although of course it is natural in Russian.
The name ‘Chinook salmon’ for O. tshawytscha is largely unused in Alaska aside from immigrants from the southern NWC, and for biologists who often use English names from outside Alaska due to their use in the scientific literature. Some Alaskans scoff at the name, in fact, considering it a mark of the cheechako or newcomer. It does see occasional use in Southeast Alaska, but again this is probably due to immigrants from further south. I do not recall hearing it from any Tlingit elders speaking in English, although younger Tlingits from Down South may use it due to exposure in Washington and Oregon. The name does seem to be relatively common the further south one travels, though of course I haven’t done any dialectal research to confirm this. Other terms according to Wikipedia that I have never heard in Alaska are ‘blackmouth’, ‘black’, ‘chub’, ‘hookbill’, ‘quinnat’, ‘spring’, ‘tyee’ (< Chinook Jargon táyi ‘chief, leader’), and ‘winter’. Essentially ‘king’ is by far the norm.
In the words of Forrest DeWitt, “that’s all I’ve got to say for now”. There’s plenty of linguistic fieldwork and bookwork to be done on salmon names in English and other languages, especially concerning the distribution of various terms in the Pacific Northwest both on the coast and in the interior. Both natural and political borders play significant roles, as well as the complex economies surrounding commercial, sport, and subsistence salmon fisheries, and I hope an English dialectologist will look into this area in the near future.
[Information on Russian terms and their etymologies is from Sasha Vovin, with help from the Этимологический словарь русских диалектов Сибири (Etimologicheskij slovarʼ russkix dialektov Sibiri) by A.E. Anikin (1997). Proto-Athabaskan and Eyak data are from various sources, including a manuscript by Jeff Leer (2008). English data and etymologies mostly from the Oxford English Dictionary, 2nd edn.. Biological information is from the Alaska Department of Fish & Game Wildlife Notebook Series as well as from Wikipedia.]