Ok, this is sort of spoiler territory for Control Resonant, but it's so rife with speculation that I don't know that I could really call it such.
Across the "Altered Manhattan" of Control Resonant, Dylan can discover several hidden outposts whose documents are archived under "Secret Organization." My initial guess at them was that they belonged to the Blessed Organization.
If you're unfamiliar, the Blessed Organization is a sort of faction that appears to be opposed to the FBC and has been involved in the creation of or at least distribution of altered items with an apparent intent to cause chaos and death.
Periodically, businesses going by the name "Blessed" something or another, will be involved in some event involving an Altered Item. The origins seem to go back to the 1990s, when a motivational speaker going by the name of Chester Bless (I'm guessing a pseudonym) would go on tour with a surf board that had paranatural properties. While the FBC was able to track down the board itself, Bless evaded them.
Notably, the motivational speaking events had a slogan talking about the Power of the Board, using the surf board's apparent ability to confer a sense of boldness and confidence in people. However, the emphatic use of this capitalized "Board," and Blessed's clear knowledge of the FBC, suggest this may have been a cheeky or taunting reference to The Board, the extradimensional entity that has been attached to the FBC since Northmoor made contact with it back in the 1960s.
The FBC has seemed to have had contact with members of the organization. In the first game, we get the recording of an interrogation with a suspected member that goes pretty horribly, as the FBC agent struggles to avoid using any Bureau terminology that he's not allowed to reveal to civilians, while the suspect seems to know quite well such terms.
Blessed is known to have sent an altered item that killed an FBC employee, mailing a fondue kit to the studio of America Overnight, a late-night radio show designed to monitor stories of paranormal phenomena and disseminate Bureau-approved narratives surrounding them. The fondue kit seemed to burn the agent to ashes in mere moments, to the shock and horror of her co-worker and, it turned out, romantic partner.
Worryingly, in Alan Wake II, Barry Wheeler, in emails to Alice Wake, says that he met Chester Bless at one of the Organization's front businesses (some sort of health club) while acting as executive producer on the Alex Casey films in Hollywood. While Barry, given what we know about him, is unlikely to be a willing participant in this violent criminal activity, he does seem to now have a substantial connection to the organization. When Alice moved out of Parliament tower, the moving boxes with the few remaining items of hers and Alan's that are left there have "Blessed" printed on them.
(It is my, and as far as I can tell, mine alone, interpretation that the "organization" that helped Alice recollect her memories from 2010 was not the FBC, but Blessed, and that her visit to the Oldest House was a separate event.)
Blessed does play a role in Control Resonant, in a side quest involving a set of speakers, which Dylan must collect. These speakers have various effects on people, ultimately seeming to put multiple consciousnesses and personalities into a single body, but among the sources of the speakers is a business called Blessed Antiques.
However, it is the very presence of Blessed in this side quest that makes me skeptical of my initial assessment of the "Secret Organization" being Blessed. At no point is this other organization affiliated with the word Blessed, and what we can gather of its attitudes and goals does not seem consistent with Blessed.
Here's what we know about the Secret Organization:
They have hideouts underneath various businesses across Manhattan, all of which seem to be part of chains (though this might be simply because of video game efficiency - Remedy didn't have the budget to make a bunch of different types of coffee shop, so every one we can visit in the game is part of the Atlantis Cafe chain, for example).
The Secret Organization appears to be well-funded, with extensive supplies including weapons and, of course, these secret hidden doors in the backs of Manhattan businesses.
Like the FBC, they have documentation that uses standardized forms, as well as some of their own terminology. The terminology is notably different from that of the FBC, such as the use of the term "extranormal" rather than "paranatural."
A letter in the first hideout you can find reminds agents that they do not have an adversarial relationship with the FBC, but further emphasizes that, nor do they have a friendly relationship with the FBC.
The secret organization has a symbol that appears like a keyhole perhaps with an eye in the upper, circular part. I've seen people compare this to the eye of the Former (who does not seem to have put in an appearance as far as I can tell, in Resonant,) though I don't know that I can draw that as a direct connection.
What I find significant about this symbol is its sort of more occult design. While I think you could make an argument that the FBC's logo is itself somewhat occult in nature (an argument that extends to the seals of other, real-world American government agencies,) the Secret Organization's icon does not read like a US government agency logo.
If I recall correctly, we only get one voice recording of a member of the agency. In it, a woman speaks with what sounds like a Russian accent, and so I've seen some theorize that this organization could be the Russian equivalent of the FBC. There's certainly precedent here: given the historical rivalry between the US and Russia, there have certainly been well-funded Russian spies in New York both when they were working for the KGB and today as part of the FSB, so if the FBC is basically the "FBI for weird stuff," then an equivalent Russian agency spying on American efforts is pretty reasonable.
That said, it's not obvious that this particular individual is indicative of the national origins of the whole organization - for one thing, I might have the accent wrong. But also, this could be some kind of NGO that works across borders.
One thing that also really differs from FBC practice is that the Secret Organization appears to have protocols for the destruction of Altered Items (or Extranormal Objects, or whatever their term is). We hear a report of an agent giving his life to see one such item unmade (I can't remember exactly what the term was... was it "dispersed?") This appears to have been a voluntary act, a sort of suicide mission, and while I've seen some speculation that this was a human sacrifice, I'm not ready to make that leap - perhaps this was less of a death ritual and more like a heroic soldier throwing himself on a grenade.
The Organization seems to be highly compartmentalized, and I'm not sure if discussion about avoiding "the French Delegation" is about an actual diplomatic delegation there at either the Consulate or the U.N., or if it's the French delegation from their own organization. If it's the latter, that would I think suggest that this isn't some Russian agency, but perhaps more of an international group.
There is a note about one of the cells having to be abandoned after the group was sold out by someone named Larry, but it's not clear to whom.
There are subtle hints, I think, that the organization might not be quite as professional as its protocols and clearly well-funded secret doors and stocks of assault rifles would suggest. Indeed, the recorded message we get has the woman complain that they've been tasked with surveillance for a very long time without relief. I imagine that a professional agency would have a system in place for rotating people out if they're just on watch duty. The recording is found in the first of these hideouts, in the Atlantis Cafe right across from the Oldest House (actually probably the one featured in the announcement trailer,) where they were tasked with monitoring the entrance of the building over lockdown.
Funnily enough, it appears the nearby laundromat was being used as a location for FBC agents to keep an eye on their own headquarters, and the two groups interacted (the Organization spotted Jesse walking in in 2019, but had no idea who she was). The woman who made the recording had an interaction with these agents - though while she identified them as FBC, they didn't seem to clock she was anyone other than a parking attendant.
So, I have the following potential scenarios:
First, that this is another country's FBC equivalent, either Russia's or perhaps a joint EU one. I'm disinclined to believe - while the members of the Organization are very dedicated and committed, there's a certain organizational messiness to it - and while that certainly isn't unheard of in government agencies, it doesn't really feel like these people have a robust support network behind them.
The second is that they are Blessed. I just don't think that the game points to that, mainly because we do see Blessed involved in the speaker quest, but at no point are these people linked with that story.
Lastly, we come to what I think is the most compelling scenario: that this is a non-governmental entity, likely funded by someone with a lot of money, but who is doing this for personal reasons (maybe ideological). Some ultra-wealthy person at the top would have the resources to build these facilities and hire people to work clearly very difficult jobs in rough conditions, but might not have their own personal history in intelligence work to know all the best practices when running a clandestine program on this scale.
Finally, as a bonus theory: here's my crazy tin-foil hat. This is absolutely just my "stitching together clues that might not have anything to do with one another" ideas, but hear me out:
What if this is being run by Alan Wake?
In the "Master of Many Worlds" video we find in... I think the Evac Zone? Or maybe the Park? Anyway, the one with Alan in it, he is wearing a jacket with a patch for "A Watchful Eye Security Company," with the initials for A Watchful Eye, AWE, displayed prominently in the middle.
The Organization's symbol does look like a keyhole, yes, but also with what seems to be an eye in it (like someone peeping in through a keyhole). Is this that very same Watchful Eye?
Consider this:
In 2012, Sam Lake (never technically confirmed, but we'll see why it's pretty clear he did) created a blog called This House of Dreams, which introduced the town of Ordinary, Maine, and was ostensibly the blog of a woman named Samantha Wells (get it, Samantha Wells, Sam Lake?) who moved into one of the abandoned houses in Ordinary and began fixing it up (evidently part of a push to repopulate the town after the vanishings in 2002). Samantha finds a shoebox filled with the poetry of Thomas Zane.
While there was a possibility that this blog's connection to Alan Wake as a game was just some creative fan project, by Alan Wake II, we had characters like Tom Zane quoting the poems found in that blog. Also, the appearance of Ordinary, Maine as a crucial location in Control seemed to point to this being made with some intimate prior knowledge of what Remedy was planning.
Anyway, the conclusion of the blog sees Samantha encountering what appear to be government agents wearing windbreakers with the letters "AWE" on them, who come to confiscate the poems.
Now, I think the general consensus is that the "Department of AWEs" was the working title of the Federal Bureau of Control, and that this was something of a retcon to make it sound a bit more plausible as the name of a government agency, and to play into the thematic idea of Control in that franchise. And honestly, I think that's probably the explanation.
But Remedy, and Sam Lake in particular, has shown a propensity for utilizing ideas he came up with long, long ago for future games. Consider how the TV show, Address Unknown, in I believe Max Payne 2, a surreal Lynchian noir, winds up more or less predicting the structure of Alan's journey through the Dark Place. (Indeed, if we assume that the Max Payne games follow the plots of Alan's Alex Casey books, could Alan have actually written Address Unknown into his own novels, and then dug up those ideas to structure his journey through Initiation?)
The point, though, is that if those windbreakers with AWE on them are not actually government uniforms but are actually the uniforms for a private security company that Alan has created (perhaps writing it into existence,) might the Secret Organization be... A Watchful Eye?
It's the biggest stretch, of course, but it's food for thought.