This is in the comic continuity, not the TV show, but at one point, Matt Murdock was outed as Daredevil. I know he turned down an invitation to the Avengers because of it, recommending Ronin to serve in his place. This was from The New Avengers a few years back (issue #11, 2005).
I failed to keep up with the story, so I don't know if this was retconned, if he took on a new identity, or much like the "history rewrite" of One More Day when Peter Parker's identity was reverted to being a secret, if something like that happened.
Can anyone provide any details, please?