The Persona series is pretty straightforward about the types of personas they include in their roster and where they come from. Personas represent the parts of humanity deep inside people that aren't seen everyday by society.
These "other selves" often take the forms of mythological beings and creatures. Using these beings, the people of the Persona universe are able to represent themselves with caricatures of human desires and thoughts. This is why a lot of the personas players see are pretty recognizable, but most of the time, they're not easy to recognize, especially for western players.
Izanagi
As the persona of the protagonist in Persona 4, Izanagi is one of the more recognizable personas in the franchise. For those who aren't familiar with Japanese mythology, Izanagi is one of the most powerful deities who is responsible for the birth of many of Japan's islands in their lore.
The name Izanagi is especially fitting with the ongoing struggle through Persona 4 where an unseen force is pushing back against the player, causing the events of the game to progress the way they do. Eventually its revealed that the true enemy behind it all was Izanami, Izanagi's counter part. In their mythology they became enemies after Izanagi was unable to protect Izanami.
Hastur
Mythology has expanded over the centuries and grown to even include modern mythos and stories like the works of H.P. Lovecraft and other more modern influences. Persona has taken note of this and also included personas from other mythos that have less to do with folklore, and more to do with literature.
Hastur is a great example of this as he is best known from the Cthulhu mythos as his half brother. Hastur has many appearances but the depiction in Persona 5 Royal is fairly accurate as he's been described as "octopoid" and is said to have multiple razor sharp tentacles coming from all over his body.
Forneus
Forneus is a staple in Shin Megami Tensei and early Persona games who takes on the appearance of a humanoid manta ray. Despite his looks, Forneus is extremely powerful and influential in the world of Hell. He's a Great Marquis who commands 29 fleets in total. When summoned, he has the power to make men well-versed in speech, while also taking away their logic. As an ally in war, he can make anyone an ally, and convince any man to attack another.
Seth
Seth is a powerful deity in Egpytian mythology. He is the son of Geb and Nut, the earth and sky deities respectively. Originally, this gave him power over the deserts and storms, as well as other things like foreign lands. Seth was heavily connected to the pharohs as well which ties well into his uses in the Persona series.
Seth served as a connector between the gods and humans, so it makes sense why he would be chosen among the many for a consistent persona in the franchise. Seth's appearance has changed over the course of the series as well to fit different descriptions of him from multiple stories.
Crystal Skulls
The crystal skulls of Persona 5 are a strange replacement for the golden hands but they serve a similar purpose. Players can recruit them to make stronger personas, extort them for money, or just kill them quickly for a large amount of experience. The crystal skulls have been portrayed in media like Indiana Jones and The Crystal Skull but their history runs much deeper than that.
There're mesoamerican myths describing the skulls as precious, ancient artifacts created by other-worldly beings. Supposedly, there are 13 skulls to be found in the world, and when they're gathered together, the secrets of the universe reveal themselves. To this day, not a single one has been found in any archeological digs, but instead they've been crafted to cash in on the hype.
Johanna
Johanna is an interesting case in the Persona franchise and real life. In Persona, she's an interesting persona because she takes the form of a motorcycle for her user to ride. This is a unique concept for a persona since they're usually humanoid and appear behind their users. She's also unique because it wasn't clear that she was a "myth" until recently. She was idolized for standing against the Catholic church and standing up for her people, but history has revealed that she might not have ever existed. There's no evidence of her existence or proof of the good she supposedly did for her fellow Catholics.
Silky
Silkies are a Scottish myth that were thought up to keep servants in check. They appear as fairies in homes, performing tasks and chores around the house, helping ideal servants and workers. The downside to Silkies being in a home is that if any workers are lazy, they will leave the home in disarray and cluttered.
Silkies can also be mischevous and play tricks on the inhabitants of the home, but that isn't too common unless everyone is lazy, according to the myth. Many people in Europe believe in the existence of fairies, whether they're Silkies, or some other kind, so it makes perfect sense that they'd appear in multiple Persona games.
Queen's Necklace
The Queen's Necklace is another special persona in Persona 5 that acts as a special treasure item, more than an actual persona. The story of the necklace does have a lot of basis in reality, since the "affair of the Queen's necklace" was a real thing that happened and sparked the French Revolution.
The folklore comes in with Arsene, the persona of the main protagonist in Persona 5. His persona is Arsene Lupin who appears in a story with the necklace, creating an iconic piece of historical fiction. The naming of this treasure item may seem strange to players who are unfamiliar with the stories of Arsene, but it's a nice detail for players who got it.
Pyro Jack
Pyro Jack is a staple character in the Persona series and most other Shin Megami Tensei games as well. He also goes by Jack O' Lantern, and is based on an Irish tale about Stingy Jack. In the story, Jack convinced the Devil not to take him to hell, but was also refused entry into Heaven. Because of this, he was cursed to wander the earth as a pumpkin headed spirt.
Jack O' Lanterns have a long history in folklore, but this story seems to stick with it the most, since people still carve Jack O' Lanterns to this day on Halloween. It's said that the lanterns help guide the spirt of Jack to wherever he needs to go so he doesn't bother any people on his way.
Unicorn
Unicorns are widespread creatures of lore that almost anyone can recognize from popular media. What most people don't recognize is what Unicorns actually look like and are about. Unicorns were originally known to have a beard like a billy-goat, the tail of a lion, and cloven hooves as well as their signature horns. Most of these details have been scrapped in modern depictions aside from the horn.
Unicorns are also very aggressive and powerful, able to summon lightning with their horn and kill humans almost instantly. This makes them a great persona since they can appear lovely and graceful on the outside, but harbor its true nature further within.