I imagine his story being more on the side of a more realistic/gritty crime drama than a superhero. Something that could fit in with season 1 Arrow or the 2004 version of the Punisher.
As a teen, his parents were murdered; but this is not what triggered his vigilantism (at least not in the way you would expect). He basically became a delinquent who constantly got in trouble up until he eventually joined the military and made special forces.
After being discharged, he tried to become a cop, but was not accepted because his psych profile said he was too much of a "loose cannon". A narcissist with delusions of grandeur. Rather than a more noble hero, his methods far more closely resemble that of a thrill killer. He quickly became bored of holding a normal job, and to decided become a vigilante. He started with killing the local drug dealer, before quickly escalating to bigger fish.
He is highly intelligent, but also sadistic and extremely theatrical with a dark sense of humor. He is the type of character who leaves very blatent calling cards. He wants people to either fear him or praise him. He enjoys taunting the police, but he would never actually harm them. He is very organized, to the point of it being almost obsessive compulsive. When things don't go as he predicts, he starts to become unstable.
He enjoys taunting the police, but would never actually hurt an innocent (he wouldn't however be above knocking out a cop and leaving him handcuffed in a rather humiliating position).
Though he appears quite psychopathic he does care about the few people he is close to. When his identity is discovered and the mob retaliates, he pretty much stops caring about leaving behind evidence and his body-count skyrockets..
Basically I am having some trouble coming up with a name/theme for the characters vigilante persona. He is very stealthy and prefers using knives over guns (not that he won't use the latter when he needs too, which is pretty often)