Dagon, also known as Dagan, was a major northwest Semitic god, reportedly of grain and agriculture. He was worshiped by the early Amorites and by the inhabitants of the cities of Ebla and Ugarit. He was also a major member, or perhaps head, of the pantheon of the Biblical Philistines. The symbol of a fish in human form was really meant to represent fertility and the vivifying powers of nature and reproduction.
The Hebrew Bible, in an attempt to vilify the opposing religion, narrates that his temple was destroyed by a human sacrifice for him, Samson. In later times, Dagon become apart of the Abrahamic pantheon, where he is portrayed as a high ranking demon in the depths of Hell as well as being the chief of the Inferno
Dagon's appearance as a sea monster in the series was likely inspired by H.P. Lovecraft's depiction of the figure, before archaeologists learned more about him. There, he is a deity who presides over the Deep Ones, an amphibious humanoid race indigenous to Earth's oceans. Also known as Father Dagon and the consort of Mother Hydra, although they are Deities, they are generally not considered Great Old Ones. He is worshipped by the Esoteric Order of Dagon, a secret cult based in Innsmouth.
"Origin: Babylonia. An ocean god worshipped by the Philistines. It's said his name comes from the Hebrew sounds for fish (dag) and idon (aon). There used to be important temples for Dagon in Gaza and Ashdod. Dagon is identified as the same as the Babylonian god Oannes. He is depicted with a male appearance, with a human's upper body and a fish's lower body."
—Shin Megami Tensei A-Mode DDS Dictionary
Persona 2: Eternal Punishment
Dagon resides in the Tower of Perception that exists in the Kadath Mandala. Zula warns the group not to listen to him chant or they would be converted to Cthulhu's cult. Both Ulala and Katsuya are temporarily converted and the party fights against Dagon. Defeating him and watching him disappear, leaving the Trapezohedron of Perception behind.
DemiKids Light/Dark Version
"A resurrected mermaid-demon with unknown powers that have yet to be awakened."