Amazon’s subversive superhero series The Boys is known for exploring what happens when you mix costumed crimefighters with corporate sponsors and the idea of being a celebrity, but the Marvel Cinematic Universe has never really been interested in exploring the levels of fame enjoyed by its vast roster of superheroes.
Tony Stark was already known all over the world before he suited up, while Steve Rogers had been an icon for decades prior to getting thawed out, but Sam Wilson can’t even get a bank loan despite saving the entire universe. The Falcon and the Winter Soldier hinted at how the various Avengers exist during their downtime, though the show couldn’t seem to decide how well known Bucky Barnes is.
Natasha Romanoff said in Captain America: The Winter Soldier that most of the intelligence community didn’t even believe he existed, but Zemo knew enough to use Bucky as a scapegoat to murder the king of Wakanda and turn him into the most-wanted person on the planet in Civil War, even though the Baron was just a very rich man and former member of Sokovia’s elite special forces, as opposed to a high-ranking official with access to government secrets.
He was a huge part of Avengers: Endgame‘s final battle as well, which characters in WandaVision evidently had an extensive knowledge of, but his level of anonymity was inconsistent in The Falcon and the Winter Soldier. Zemo had him pretend to be the silent assassin in Madripoor because he was too well known to go undercover, but he can still make friends and go on dates in America without being recognized, even though law enforcement obviously know who Barnes is after they stopped him and Sam outside Isaiah Bradley’s house before apologizing for interrupting a pair of bickering Avengers. As such, it seems to be entirely based on whatever suits the narrative at the time.