Wikipedia says
A superhero or superheroine is a stock character that typically possesses superpowers, abilities beyond those of ordinary people, and fits the role of the hero, typically using their powers to help the world become a better place, or dedicating themselves to protecting the public and fighting crime.
So yes, he is definitely dedicated to protecting the public, but it feels wrong to call him a super hero. What do you think?
I would say no, only because he does it all in his own name. One of the key features of a superhero is the idea of separation of identity, which Grandmaster Skywalker* does not do. Not all superheroes wear masks, but even the ones that don’t usually have some form of alternate identity. (Reed Richards, for example; everybody knows who he is, but it would be weird to call him by his real name while he’s in costume.) I would say that Luke Skywalker is a hero, but not a _super_hero, specifically because he does not present himself as such.
*Grandmaster Skywalker, founder of the Yavin IV Praxeum, etc. etc. Fuck MouseWars.