Life's too short to limit oneself to just one part of reality.
The Dark Six are worshiped in Eberron, just as real or fake as any other faith. It is not their existence that fuels the power they grant worshipers, but faith itself.
But things are a little different in Skyrim.
Sovereign of Wave and Whelm
The Devourer's avatar in Skyrim is an Argonian man named Devours-The-Waves. Wielding battleaxes in place of the trident that he left behind, he also favors frost and shock Destruction magic, particularly leaning towards frost, and Alteration magic in place of traditional armor.
It is the guidance of the Serpent Stone that anchors the Devourer to Skyrim as it does for the Mockery.
Sovereign of Rage and Ruin
The Fury's avatar in Skyrim is a Breton or Dunmer - she favors two forms - and each embodies a different part of her being. She is the patron of barbarians, bards, artisans, and craftsmen. In her Dunmer aspect, she relies on fury spells, lighter armors, and fast one-handed blades to mimic the rapier she left behind in Eberron. In her Breton aspect, she favors the cities, practicing smithing and enchanting and relying on her words over her weapons.
In either case, she anchors herself with the Lord Stone (like the Keeper) and keeps the Lover Stone on the Aetherial Crown in her back pocket.
Sovereign of Death and Decay
The Keeper is both the one who takes the dead and the one who keeps them from Dolurrh...and considering how badly that plane sucks as an afterlife, he believes that he's doing them a favor. He appears as a Bosmer, standing the shortest of the Dark Six in this realm. Naturally, he believes wholeheartedly in necromancy magic as his specialization, but he is not weak and alone once his undead are felled. Instead, he favors greataxes over his missing scythe...and all of this assumes that you notice him to begin with, as he is a stealthy figure who leaves pockets picked in his wake. Due to being what he is, he also hoards food and ingredients to use later.
The Lord Stone anchors him as it does the Fury, but his backup in the Aetherial Crown is the Ritual, for he loves anything that lets him scam his own magic.
Sovereign of Betrayal and Bloodshed
The Mockery is the stealth archer of your dreams...or he would be, if he bothered picking up a bow. Instead, he appears as a Redguard who loves close-combat stealth and the feeling of sliding a dagger into an unsuspecting ribcage. Here, daggers replace his kama, but he finds them to be similar enough in execution to not worry about it. While poisons coat his blade, he supplements it with paralyzing, fear, and fury spells for his enemies and invisibility spells for himself.
The Serpent Stone anchors him as it does the Devourer, but the Shadow Stone aids him from the Aetherial Crown.
Sovereign of Magic and Mayhem
The Shadow has never existed on its own, being defined entirely as the literal cast-off shadow of Aureon. But it finds that in Skyrim, it carves its own path without that bastard burning a path first. So it appears as an Altmer, the most magical-focused race in modern Tamriel, and focuses on all five magic schools: Alteration, Conjuration, Destruction, Illusion, and Restoration. It doesn't care what spells it uses; in fact, it loves the variety. Why specialize when you can learn it all? In place of its favored quarterstaff, it uses the staves of Tamriel for when its magicka runs out, and it finds joy in enchanting its own.
The Atronach Stone is an important anchor for the Shadow in Skyrim, enabling it to remain in this realm and stand on its own.
Sovereign of Chaos and Change
The Traveler is defined by change and oddity. They are not malicious, it's just that chaos tends to upset the whole status quo. That's the point, after all. Their avatar in Skyrim is a Dunmer, though they could appear as truly anything. They were able to keep their scimitars and dual-wields them here, but they also love unconventional weapons like the Wabbajack or the spider scrolls found in Solstheim. They armor themself lightly and sneak around just to appear somewhere strange, though they also love throwing around an Illusion spell or five.
The Shadow Stone anchors them, but they also have a soft spot for the Tower Stone's power and carry it with them in the Aetherial Crown.
My favorite part of any fictional setting is investigating what the religions and gods have going on. And certain groups become my favorite bunch of bastards, especially ones that are outwardly evil. I love seeing why people would worship gods that get called evil and I love seeing settings where faith and belief matter. But the Devourer's section is the shortest because I hate him lmfao.
Plus, with Skyrim's whole religiously-charged atmosphere, it's really funny to just add foreign gods to the whole mess and see what happens.
Practically speaking, I think various gods would handle competition differently. The Devourer would not particularly enjoy any trying to claim dominion over his domain of natural disasters and storms and the sea, leading to conflict with Kynareth and her worshipers. The Fury would probably be more likely to work with other gods and Daedric Princes like Dibella, Mara, and Azura. The Keeper is probably going to involve himself in the conflict between Arkay and Molag Bal. The Mockery is going to bristle at the idea of honoring something like Sithis through killing but equally throw tomatoes at Talos statues. The Shadow is going to spend the entire College of Winterhold questline staring at the fourth wall while everyone keeps talking about this Magnus guy. The Traveler's just gonna show up in places and see what they can change. Stuff like that.
In any case, these were a fun batch to design.
(Divider by @saradika-graphics)