Ashen Covenant

Ashen Covenant is a living contradiction - a semi-organized religion of anti-theistic creed, with priesthood whose rituals are little more than an industrialized sacrilege against all gods. Good, bad and ugly alike. Ashen Covenant seeks to end all religious worship, despite indulging in plenty of its own - with the hypocrisy of that fully embraced by the followers and 'deities' of the Ashen Covenant alike.
Ashen Covenant is often considered to be the largest and most organized of all proscribed religions of the modern Mankind (although it is technically not, if only due to being the 'state religion' of a single Throne World). It's worship is actively suppressed (typically through summary execution) in majority of the countries outside of Gehenna. This is one of the very few things in which the Church of the Highmost, Temple of the Seven and the Cults of the Ascended see eye to eye.
Even the followers of the Oneiric Choir and the Terminal Sun will actively act against the Ashen Covenant operations when they are discovered. As the result, it seems to thrive the most in the countries who are characterized by their generally low level of religious fervour, and lack significant presence of large religions who are busy waging an open warfare on the Covenant.

Structure

There is no standard organizational structure for the Ashen Covenant. The only thing that's universal is the presence of one of the Demon Lords at the top of every competing hierarchy (or anarchy) of the Covenant. They reign supreme over their segment of the Covenant, typically akin to gods of normal religion - despite being de facto something extremely close to what the rest of the multiverse considers a demigod.
One demon lord might prefer the relatively standard model of secluded cults composed of a single leader, a handful of disciples and a greater number of believers. Other will prefer to mock an organizational structure of one of the religions that it opposes. It's hard to find any form of central dogma on that field, as every newly emerged demon lord will probably have different set of ideas on that field.
The glue that keeps the whole thing together are typically numerous lesser demons (archdemons or not) who are the ones that get summoned by various sub-cults of the Ashen Covenant, and are expected to teach 'their' cultists how to best further their demon lord's goal. This allows the Ashen Covenant to operate on the multiversal scale despite their 'headquarters' in Gehenna being de facto isolated.

Cosmological Views

The Ashen Covenant, to say it briefly, doesn't care about the creation of the multiverse and the way it operates on a daily basis. To them, the worlds exist - and that's all that they really need to know. They are much more busy profitting on the guillible and pursuing even greater power. There is only a very small field for theology in all of that, especially as they tend to treat theological disputes as waste of time worth only of contempt.

Ethics

Ashen Covenant's key moral teaching is their absolute lack of moral teachings. In fact, the behaviour that the demon lords appear to be promoting is almost uniformly a complete reversal of what passes as expected behaviour of pretty much every religion out there. The perfect cultist of the Covenant is utterly amoral, and ready to do every imagineable atrocity for their own sake.
In short, slaughtering an entire town just to steal a treasure from the vault of the local noble will make your demonic patron reasonably impressed with your dedication. And the more creative you were with your massacre, the better. The same can be said about most imagineable atrocities - murder, rape, genocide and even inflicting fates worse than death on your enemies are not only tolerated but actually rewarded by the demon lords.
This is due to the core pillar of the Ashen Covenant's beliefs - its violent anti-theism and contempt for all forms of religions. Demon Lords reward all acts against religion doubly well - and throw in some additional points for acting against the religiously-enforced system of local believes, and by creative forms of sacrilege. Their anti-morality at least partially stems from the fact that religions often present certain forms of morality, so its guilty by association.

Granted Divine Powers

Ashen Covenant grants powers, although naturally words such as 'divine' is strictly forbidden. Demon Lords are by multiversal definition demigods (although referring to one of them that way is in the presence of their servants or the Demon Lords themselves is a very creative form of suicide), and thus they are capable of empowering certain inviduals that has somewhat drew their attention.
Unlike more traditional religions, most demons can to a degree empower mortal followers of the Covenant through a variety of pacts, resulting in certain character classes being created by the System - all of them intrinsically connected with the Covenant as a whole.