My take:
Absolute Zero I expect is secret, or rather, "Top Secret".
Argent Adept is public, a la Dr. Stephen Strange, where he's on a different level and far beyond identities now.
Beacon/Young Legacy: As per dad, I imagine.
Bunker I expect is similar. Both known to military brass, that's about it.
Captain Cosmic, both as an analogue to Green Lantern Hal Jordan, and as a masked man himself, is likely a secret identity type who is struggling to pay any attention to his job as a barrister.
Catastrophe, every time her abilities are seen, runs for it. I think that does a fair job of keeping the full breadth of her identity from being revealed. Card art also now shows full costume with oversized goggles-- secret ID for me! Same for Verge.
Chrono-Ranger: Nothing to hide. Jim is Jim! Just with a robot arm and a time-travel device.
Doctor Medico: Secret ID. Mask, day job, concerned (if still reckless) father, he's a secret.
Expatriette I assume is public ID.
Fanatic is sort of N/A. Her identity is Fanatic/Helena. Angel is all she is now.
Guise is a secret ID. Ish. I guess. Sure.
Haka is Haka, as well. Aata Wakarewarewa is definitely public, as the urban-legend-man he is.
Idealist is a child and masked, definitely kept secret (and shouldn't be allowed to fight crime! Irresponsible, dad!)
K.N.Y.F.E. I'm going to assume, despite the transparency of her visor, that she also exists in a "top secret" paramilitary sort of existence and call that Secret.
Legacy I would've guessed is secret (Superman rule), but if Christopher says public, it's public!
Mainstay has a mask, has a job, his ID is secret.
Man-Grove, by time of Tactics, is hero-ish. But he's definitely public ID-- as far as those who know of him, anyway.
Mr. Fixer is secret. Or was until Tactics. From his bio and the fact he had a publicly respected business, I expect he kept under the radar and somehow his baseball cap did a good job of concealing things. Further suggesting this to me is the mask he adds in the Dark Watch card after his resurrection-- to further protect his identity!
Naturalist is a secret ID. Firstly, he's dead. Secondly, he's wholly masked. I'm going with that.
Nightmist: Considering her years spent in mystical study, and her apparently permanent state of shifting into shadows, and the permanent glowing white hair and eyes look, I'd expect that she's eschewed the variance in her identity. Which sucks-- having her as a private eye secret ID would be great! So, while possible, I'm doubtful.
Omnitron-X: Clearly public. Nothing to hide here-- robot body, looks like an adorable Omnitron, that's the end of it.
Parse is private, I think. As someone obsessed with data collection, I imagine she might guard hers well. On top of that, it seems she's new on the scene, which means even with her thrown-together-adventurer outfit of "yep, these are just my work clothes", she's not had too much a chance to be exposed yet. Hope she costumes up!
Pinion/The Matriarch, I think, is private. Her mask allowed her identity to be a secret, which I'm sure made for good drama during the reveal with Tachyon, but it's not clear if she ever got put away-- especially since she still has the mask in her transition to Goodliness. I suspect she's managed to maintain relative secrecy to the world at large, if not the hero community.
Ra is secret in a Donald Blake/Thor or Shazam way-- transformation hides things well. That said, Ra hisself is definitely public, but Blake or whoever Tactics-Ra is are both not known.
The Scholar is as the Scholar does, so, public.
Setback is just lucky enough that his identity hasn't been exposed-- he's got the mask, and Pike Industries isn't certain where that escapee got to, which all inclines me to say he's kept it hidden. The mask also infers it.
Sky-Scraper is a Thorathian. Ain't no hiding that.
Tachyon appears VERY public, based on the Freedom Four #1 comic and her carefree nature about her abilities at work.
Tempest I assume is public-ish, as an undeniable alien.
Unity I think is semi-private. I think people may have suspicions from her college years with the robots, and her flimsy disguise (big goggles, mostly), but I think she's trying to keep it on the down-low. I tend to always err on the side of keeping-it-secret unless evidence implies otherwise.
Verge, as per Catastrophe, Secret ID.
The Visionary is also, I suspect, marginally public knowledge. As someone out of time and space, I feel she keeps herself aloof and unknown, but she herself isn't hiding per se.
Wraith is definitively secret ID: until it's all revealed anyway by Tactics-time.
Writhe was locked up. He's been exposed. I doubt his ID is secret. That said, I imagine he's basically permanently Writhe now, so.
Summary:
PUBLIC:
- Argent Adept
- Beacon/Young Legacy
- Chrono-Ranger
- Expatriette
- Fanatic
- Haka
- Legacy
- Man-Grove
- Nightmist
- Omnitron X
- The Scholar
- Sky-Scraper
- Tachyon
- Tempest
- Visionary (ish)
- Writhe
SECRET:
- Absolute Zero
- Bunker
- Captain Cosmic
- Catastrophe
- Doctor Medico
- Guise
- The Idealist
- K.N.Y.F.E.
- Mainstay
- Mr. Fixer
- The Naturalist
- Parse
- Pinion
- Ra
- Setback
- Unity
- Verge
- Wraith
CONCLUSION:
16 Public
18 Secret
Fun Conclusions:
Freedom Five + Unity:
4 Secret (AZ, Bunker, Wraith, Unity), 2 Public (Legacy, Tachyon)
[until Tactics: Wraith becomes public ID, then 3/3)
Prime Wardens:
1 Secret (Captain Cosmic), 4 Public (Argent Adept, Fanatic, Haka, Tempest)
Dark Watch:
3 Secret (Mr. Fixer, Setback, Pinion), 2 Public (Expatriette, Nightmist)
The Sentinels:
3 Secret (Doctor Medico, The Idealist, Mainstay), 1 Public (Writhe)
I also doubt Fixer brags too much though, so some people just might not connect the dots.