When it comes to superhero names, Matt Murdock's Daredevil doesn't really describe what kind of hero he is. Not many would describe Daredevil as a reckless hero as the name implies. However, despite using the moniker, he admitted it doesn't make a whole lot of sense.
Some superhero names are obvious: Ororo Munroe can manipulate the weather, therefore she's known as Storm. Meanwhile, Bruce Wayne dresses like a Bat and is known as Batman. It's simple. With Murdock, Daredevil really doesn't do his mindset justice. The blind hero is very calculated and has radar sense, so maybe a more appropriate name would have been the Dolphin (or even Batman). But, since debuting he's kept the name Daredevil. Even Matt knows how ironic calling him Daredevil is.
The pages of Marvel Comics #1000 featured numerous one-page stories starring both heroes new and old from the pages of the comics. In 'The Devil's Brand' by Joe Quesada, Kevin Nowlan, and Richard Isanove, Daredevil sits atop a roof as he has a conversation with a cameraman. The bystander calls him the Man Without Fear, which leads Matt to monologue about his name. He says he's embraced the Daredevil codename "because I love the irony." When asked about it, Daredevil explains that the name usually implies a sort of recklessness, while he's "the furthest thing from it," since he is always cautious, takes the temperature of every room and attacks at the exact right moment.
There is something deeply ironic about a character being called Daredevil having the opposite fighting style and mindset. When the cameraman presses him more on being the Man Without Fear, Daredevil tells him the name is funny because "it's not true... I'm afraid all the time." In a somewhat epic ending to the small story, Daredevil lunges off the roof and admits "It's the only thing that keeps me alive."
Matt admits the Daredevil name - or the Man Without Fear designation - doesn't perfectly encapsulate who he is or how he acts as a hero. Despite that, he's adopted them. However, that doesn't mean he's suddenly in line with the names. He's not a daredevil, nor is he without fear. Instead, his fear is what drives him. While the story is only a single page, Quesada, Nowlan, and Isanove do a masterful job at delving deeper into Matt's mindset. He might be Daredevil, but he's no daredevil.