I'm misunderstanding your point. I'm not saying that the characters should idolize gods or anything, just that something like "Oh, my persona is a thunder god who was worshiped thousands of years ago? I also saw a Disney movie with him in it. Neat." wouldn't be too far off.
But I don't think they need to outright acknowledge it like that because it seems unecessary. The point is that the shape of one's Persona is shaped by the ego. It is an archetype of the collective unconscious, something which we'd call a shared network between all of humanity. The Persona itself represents your public image. The word is, obviously, related to the word person and personality, and is derived from the latin word "mask". So the persona is the mask you put on before you show yourself to the outside world. Although it begins as an archetype, by the time we are finished realizing it, it is the part of us most distant from the collective unconscious. The reason why they take shape of myths, folklores and legends are due to the collective unconcious -- It can appear in dreams as a scarecrow, atramp, or as a desolate landscape, or as a social outcast. To be naked in a dream would symbolize a loss of persona. It's all symbolic and hence that's the reason why it's never truly acknowledged in the games. Symbolism is something that is implemented behind the outer layer to provide an underlying and depth and meaning to the game's design, not just in terms of the Personas, but the tone, music and level design.
It's usually something for the player to acknowledge and comprehend.
It's sort of the same reason why Silent Hill 2 doesn't outright have a character walk up to James and tell him why this town is trying to kill him, or why these monsters look the way they do.