Like Kindred, Kench's form changes based on who is seeing him. His current form came from a Bilgewater gambler, who, as he lives in/near a sea port, must of been more used to water creatures, so Tahm appeared as a giant catfish type thing.
But this begs the question, what does he look like in other areas? In Bilgewater he is called the river king, but what about in Damacia? Ionia? Kindred is called other things in other cultures. They are called Ina and Ani in the west, Farya and Wolyo in the west, but they are always Kindred everywhere(as seen in "The Good Death", their words too.). I think this applies to Tahm.
Everywhere may know Kench, but is he always the RIver King? I doubt it, as he is a crossroads demon. Why would the arid Shuriman wastes consider him a catfish or other water creature if there are very few places to get water? Wouldn't a scorpion-esc or one of the giant camel things be a better animal to be based off of? Each region has different views of vice, so every region views Tahm differently.
Evidence from the Q&A
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Tahm Kench is one of the many names given this creature. That form and name is unique to Bilgewater. (Notably Bilgewater has a very different view on vice than our other locales.)
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_Where did Tahm come from? Did he cross over from another realm, like the voidborn? Was he wildlife now transformed beyond recognition, similar to Gromp? Did he simply exist since the beginning of time? _
His is tied to the foibles of mankind-- and his current form is especially tied to vices of Bilgewater.
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_Within the story, how did Tahm acquire his name. Did he name himself or did someone else? _
Tahm Kench is the name commonly given this spirit in Bilgewater. The real question is what is the gambler's name.
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He's the 'River King'. Why not incorporate anything river related to Tahm, in gameplay, or is this just part of him as an overall character?
Like many things about Tahm think of a river metaphorically."
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Tahm says that "the world is one river, and i'm its king. Ain't no place i can't go, aint no place i cant go again." Is this true? I find it hard to believe that Tahm can go anywhere in Shurima. And how does that work anyways? Does he burrow through the ground? Not every lake, river, ocean, pool and oasis is connected, so either he burrows through the ground, or he teleports. Maybe there is a massive underground ocean that only he knows of?
There is an ocean of darkness in every man's soul."
So in essence he is a crossroads demon, apparently the only one in runeterra, and the reason he is a river demon is that in Bilgewater, water is the main way to get around. So he would take residence in the water when he is feeding there. I hope this helped.(or at least didn't cause too much pain...)