I'm surprised that some popular ones weren't covered by other answers here first. There are several superheroes that meet those two conditions (that weren't already mentioned by others):
- Ant-man + Wasp: In both of the Ant-man movies it doesn't appear that their identities are public. This extends to all versions of Ant-man including Hank Pym and Scott Lang (although it might now be known).
- Black Widow: Her identity as an assassin was completely hidden from the public until she leaked the S.H.I.E.L.D. files in Captain America: Winter Soldier
- Ghost Rider: In the S.H.I.E.L.D. series, Robbie Reyes is the hidden identity (similar in the Ghost Rider movie with Nicolas Cage as Johnny Blaze).
- Inhumans: This one is messy, but Inhumans, in general, hide their identity; so much so, that the entire civilization moved to the Moon (Attilan). They also have a secret settlement in Nepal (Afterlife). Now, most Inhumans are widely unknown to the gen pop until fish oil supplements contaminated with Terrigen begin causing Terrigenesis in humans across the globe. There's a bunch of Inhumans that S.H.I.E.L.D. helps to hide their identities and get their powers under control. The whole show (Agents of S.H.I.E.L.D.) was based around this concept halfway through and is a good watch.
- Black Panther: His identity is known only to his people, but not the rest of the world; he's only known as T'Challa and ruler of Wakanda. Although, this kind of fits opposite to your conditions (to the world, his person is known but, initially, not really his hero). Now, we can assume that most people presume his identity as both.
- Soldiers? (e.g., Falcon, War Machine): While their identities are not really secret, they don't go around telling everyone. They are military personnel and so there's some level of secrecy to their identity; not sure if this classifies as a secret identity under your conditions. Agents of S.H.I.E.L.D. also touches on super soldiers with some walking the line between hero and villain like Deathlok.
Then there are also unknowns (e.g.,
Doctor Strange, Vision, etc.): We don't really know how "known" these heroes are and if their identities are out there in the public. I wouldn't classify these as secret identities, but instead as secret heroes.
Note, however, that some of these superheroes do (or may) eventually show their identity, but they are/were unknown for a while to the public. Many of their identities are known to the government, S.H.I.E.L.D., friends, or family.
There are also hundreds more superheroes in comics that have secret identities, but the MCU, very few of them keep secret identities or they have them exposed in some way.