Dagon 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 Hebrew Bible, in an attempt to vilify the opposing religion, narrates that his temple was destroyed by a human sacrifice for him, Samson.
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.
"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."