Psyche was the youngest daughter of the king and queen of Sicily in Greco-Roman mythology. She was the most beautiful person on the island and suitors flocked to ask for her hand. In the end, many boasted that she was more beautiful than Aphrodite herself, and Aphrodite sent her son Eros (Cupid) to transfix her with an arrow of desire and make her fall in love with the nearest person or thing available. But even Eros fell in love with her and took her to a secret place and eventually married her and asked Zeus to make her a goddess.
Psyche's butterfly motif is a play on words. The word "psyche," along with being a character's name, can also mean "butterfly" and "soul." The goddess Psyche and souls were thus frequently depicted with butterfly wings.
There are unused Persona Slots for Psyche (as well as a Picaro variant) in Persona 5 Royal. There isn't a model for it, and attempting to use a skill will soft-lock the game.
Both versions have no weaknesses or resistances, much like Psyche in Persona 3.