@Nex:
At this point, all of their identities are already known to the government. In the MCU, there's not a single hero that the government has no clue on. it would make more sense if there was 5000, because the whole point is the identify anyone with powers and what those powers are. There's no need for that in the MCU.
The Government knows who Iron Man, War Machine, Captain America, The Hulk, Black Widow, and Hawkeye are.
Meanwhile, The Government knows Thor as Thor. He's now living on Earth as per the end of Thor 2. We don't know how they're going to handle that at this point. Might they align the movies more with the comics and have Thor adopt a secret identity a la Donald Blake?
They don't know who Falcon is either. Or more accurately, they don't know Sam Wilson is now unofficially heroing in the Falcon suit. As far as they know, he's retired. The fact that he wasn't on S.H.I.E.L.D.'s Radar is why Cap went to him.
The World doesn't yet know who Quicksilver and the Scarlet Witch are from everything we know. Also, we know Dr. Strange was a person of interest to HYDRA, but we don't know how much they know about him.
Also, Vision, Ant Man, Daredevil, Luke Cage, Iron Fist, and Jessica Jones all have upcoming appearances in the MCU, and there are Rumors about a possible Black Panther as well as Captain Marvel film in the works. Marvel also has the rights to Ghost Rider, Blade, and Punisher who can be introduced into the MCU not to mention the rurmors about Spiderman also possibly joining the MCU as well.
As Robby said tho, there's more to it than JUST secret identities as well. You can easily set it up like Tony and the Government want to basically have Registration be a Government operated task force of Superheroes. IE, if you want to be a Superhero, you have to sign up with and work for the US Government. It's made ILLEGAL for anyone to operate as a hero unless you're part of the Government's special Super Squad. With what happened with S.H.I.E.L.D. in Cap 2, I can already see Captain America not liking that concept.
That's why I think we DEFINITELY need Avengers 3 to still be the Infinity War and save the full-blown Civil War for Avengers 4. Cap 3 needs to have Tony laying the seeds of what will become Civil War, without that movie involving him and Cap directly at-odds. Civil War needs to be as deeply setup as the Infinity Stones are now when it gets paid off later.
Plus, they then have PLENTY of time to world build some more and get more players on the table for the actual "War".