Rayleigh’s epithet, Mei-Ō (冥王; lit. dark king), is the Japanese word for Pluto/Hades, the god of the underworld in ancient Greco-Roman mythology”.
According to Wikipedia “Following their victory, according to a single famous passage in the Iliad (Book XV, ln.187–93), Hades and his two brothers, Poseidon and Zeus, drew lots for realms to rule. Zeus received the sky, Poseidon received the seas, and Hades received the underworld, the unseen realm to which the souls of the dead go upon leaving the world as well as any and all things beneath the earth”.
So it could refer to how Rayleigh and Roger split their rule, Roger being the Pirate King and Captain, and Rayleigh being the Dark King and vice-captain. One working and ruling in the shadow of the other in the “unseen realm”.
I just went down a Greek mythology rabbit hole and guess what! Poseidon is not only the god of the sea, he’s also the god of earthquakes! Could Whitebeard be the Poseidon to Roger’s Zeus and Rayleigh’s Hades? Zeus is the king of the gods, Poseidon rules the sea and Hades rules the unseen realm, three equal brothers split by the luck of the draw.
Upon further digging the war that made Zeus, Poseidon and Hades the new Rulers was against their father Cronus.
Cronus came to power by, as the leader of the Titans, overthrowing his own father Uranus known in Roman mythology as Caelus or in english celestial. To quote from the article on Cronus: “After dispatching Uranus, Cronus re-imprisoned the Hecatoncheires, and the Cyclopes and set the dragon Campe to guard them. He and his older sister Rhea took the throne of the world as king and queen. The period in which Cronus ruled was called the Golden Age, as the people of the time had no need for laws or rules; everyone did the right thing, and immorality was absent”.
Now what do we know about Rocks D. Xebec? He led a bunch of monsters (titans?) against the Celestial Dragons in an attempt to become the king of the world, but he was stopped at God Valley by Roger (Zeus?).
*Theory by Bitterbumps