The neighbourhood is called hell's kitchen therefore they called him the "devil" of hell's kitchen as a reference to the place he saves. Devil like he is the one in control there. That's how I understand it.
by the way he acts and dresses he's considered the devil, and he's mainly situated in hell's kitchen, so he's dubbed the devil of hell's kitchen. In the show however he was framed for the fisk bombings of the russian districts and so was dubbed the devil of hell's kitchen
