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A man lands on watery, tropical alien planet and encounters creatures. These aliens try to speak English, but pronounce each word starting with the H sound. I think the aliens may have had tentacles, and when the man first meets them he is offered a drink from a pouch an alien wears on his abdomen. The man gradually wins the aliens' admiration and wins a tournament, but his alien friend dies. The man is proclaimed the “hnkeraput” or something like that.

Likely written in 50s-70s and definitely before 1977. It was not part of an anthology and was by likely a minor writer.

I'm pretty sure you're thinking of C. S. Lewis' Out of the Silent Planet. It was first published in 1938, but it has been in print ever since in many editions.

It's set on Mars, but most of the story (and all the bits you mention, above,) happen deep in one of the canyons that from Earth we see as canals, and they're wet and tropical.

The main Martian race (there are three) that Ransom – the main character – encounters has a language which begins many words with an "H". They call themselves the "Hross" and the word for any intelligent being is "hanu" Ransom goes with his Martian friends to hunt a dangerous beast and kills it and is declared an "hnakrapunt".

The part about the drink from the pouch is also there:

In its hand (he was already thinking of its webbed fore-paw as a hand) it was carrying what appeared to be a shell – the shell of some oyster-like creature, but rounder and more deeply domed. It dipped the shell in the lake and raised it full of water. Then it held the shell to its own middle and seemed to be pouring something into the water. Ransom thought with disgust that it was urinating in the shell. Then he realized that the protuberances on the creature's belly were not genital organs nor organs at all; it was wearing a kind of girdle hung with various pouch-like objects, and it was adding a few drops of liquid from one of these to the water in the shell. This done it raised the shell to its black lips and drank – not throwing back its head like a man but bowing it and sucking like a horse. When it had finished it refilled the shell and once again added a few drops from the receptacle – it seemed to be some kind of skin bottle – at its waist. Supporting the shell in its two arms, it extended them towards Ransom. The intention was unmistakable. Hesitantly, almost shyly, he advanced and took the cup. His fingertips touched the webbed membrane of the creature's paws and an indescribable thrill of mingled attraction and repulsion ran through him; then he drank. Whatever had been added to the water was plainly alcoholic; he had never enjoyed a drink so much.

In Out of the Silent Planet (1938) by C. S. Lewis (the first novel of his Space Trilogy, the Hross race native to Mars seem to have all their words start with h. When Ransom, the recently arrived human protagonist, is first learning from the hrossa (plural of hross), we get this:

It named this harandra. The low, watered country, the gorge or canyon, appeared to be handramit. Ransom grasped the implications, handra earth, harandra high earth, mountain, handramit, low earth, valley.

The hrossa also wear liquid-carrying vessels on belts around their waists.