Xavier Remington 
The Devil is the Chief Archdemon Of The Omniverse, and Emperor Of Hell. Technically he exists simultaneously in a plethora of Multiverses just as we exist in a variety of parallel Universes. So our Devil is merely the Archdemon Of The Multiverse. However there is most likely a dormant entity, or one will be born someday, with all the memories of his parallel Multiverse selves. In the meantime he is the Master Of Evil in this Multiverse, and deals in darkness across all manner of parallel Universes. Something that’s realistic for a five dimensional being such as himself. Just in case you thought he, and his demons, don’t really seem to have much to do on Earth.
The Devil’s domain of darkness includes every reality where Earth exists but anywhere a planet has sapient life to corrupt. In some cases the forces of good may block him on a given planet but it’s thought he is the Devil on millions of planets across the great galactic expanses of any given Universe. He, and his demons, battle the forces of righteousness on these planets while also devising trillions of Armageddon’s as well. There’s also the creation of demonic based entities such as demi-demons, vampires, werewolves, etc. Each planet having it’s own unique demonic monsters!
On these various planets in a multitude of realities the Devil goes by different names, and has varying legends written about him. It will be interesting to explore the stars, and meet extraterrestrials to compare Biblical notes. The similarities in stories may startle even the most logical supernatural skeptics!
Wait, so there are multiple Devil’s?
Yes Lucifer, and his fallen Angels were forced to the lower dimensions which naturally splits them into multiple entities. As an Archangel the Devil became a plethora of five dimensional beings ending up in their own Multiverses. Various Demons only became 4-D entities living in a variety of parallel Universes. So there are multiple Hells in the 5th, and 6th dimensions.