Dagon is a unique short story in Lovecraft's significant body of work. It is not considered Cthulhu Mythos canon, but it is an obvious forebearer. The story is told in flashback form by a madman, driven insane by nightmares of some unspeakable terror sighted in the distant past. Shipwrecked on a "slimy expanse of hellish black mire," our hero wonders the coast for days, hoping for rescue. Eventually he journeys inward, finding a stone relief with bizarre hieroglyphs depicting sea-dwelling humanoids and various normal sea creatures. While he looks on, a massive beast rises from the depths behind him and heads immediately for the stone tower, wrapping its arms around it and uttering strange noises in what appears to be a prayer.
The name "Dagon" is not the beast's name, but rather a Philistine fish-god. The story's protagonist wonders if "Dagon" might be real in some form, and perhaps he just saw it. "Dagon" appears in Lovecraft's more popular canonical Shadow Over Innsmouth, in which the Deep Ones are said to worship said deity. In that story, however, the name "Dagon" is applied to Cthulhu, most likely an attempt by the Innsmouth residents to apply an existing name to their undersea god. Thusly, the Dagon of Innsmouth is not the Dagon of Dagon.
I rather prefer to think of Dagon as kind of an outgroup to the Cthulhu Mythos, seeing as it shares so many commonalities with the latter body of work. Indeed, the fish-people of the stone tower may well represent the Deep Ones with whom the citizens of Innsmouth made their infernal pact.
My take on Dagon is still evolving, but the final draft will look similar to this. Keeping with my interpretation that Dagon has some connection to the Deep Ones (and Cthulhu), I tried to make it a tetrapod that would exist somewhere in the depths, but one corrupted by the Deep Ones. If humans turn into fish-people, what would a whale turn into? Or a crocodile? I don't know if I'll keep the arthropod legs, but I do like how they give the back half something to do. Let me know what you folks think! I am open to suggestions on how to improve this design.