Azrael wasn't his given name. It was a title.
Alezander was born in Litari, but after suffering from amnesia he cannot recall his adolescence and childhood years until he moved to the Circle capital of Belvar after the events of the Vampiric War.

His parents were runaways - his father was an impoverished aristocrat while his mother was a daughter from a famous, but horrendous merchant's guild in Litari's underworld. Only to seek refuge, his parents left the country to create a new life suitable for Alezander to live in comfortably. In his teenage years, Alezander was a fairly active young boy, who was filled with energy and happiness. Though, him and his family weren't very wealthy and often had trouble to maintain food and medicine to fend from illness.

Alezander often resorted to thieving and other inconspicuous jobs that led him to trouble. He worked in a small thieves guild in Belvar in order to provide medicine for his sick father. He was later given the title of "Azrael" for his ferocious fighting power, and as well as his intimidating gorgeous looks during his young age. He was skilled in many heists and deemed himself richer than many of the wealthy families in Belvar.
Yet, he decided to quit a few years after he achieved infamy. The death of his parents due to illness greatly affected Alezander's well-being. He simply decided that he's put down his life as a bandit to join the military in Cathal for a while. 

His skilled were useful in the army but Belvar and Kingdom of Cathal were at a golden era of peace - where Azrael's skills weren't used for anything except for being a messenger or guarding the borders. The Italian was offended that his skills were provided to be "useless" to the city and later withdrew from the army to act as a mercenary. He created the popular Mercenary's Guild located at the heart of his home; but he simply never appears there to uphold it's business only because he's too busy being on the run.

Cagliostro wanders around all across Belvar; only because he was still a wanted man after all these years. Somehow none of the guards were able to catch him even for his older age.

The Heroes of Belvar

Cagliostro lived his life in Belvar, but it was the first time in years that Azrael had to actually force himself to fight once again and keep his home from being lit up in flames.

After the absence of the guardsman and Alphonse due to an upcoming war among the capital of Cathal, Belvar had no choice but to handle most of their political needs to the higher-powered nobles who sought for total control over the city. And knowing Cagliostro - who didn't enjoys these snide aristocrats had refused to officially hand over Belvar to them even if it was a temporary time. He and many other Belvarian citizens were already trying to prevent another civil war in their very own home.

Azrael had been friends with a butler, who has befriended nobles in the Zane household which has given Cagliostro an advantage to the situation at a political standpoint. However, the man was more concerned to Belvarian civilians - who were in the middle of a civil war outbreak among other noble houses across the city. Amongst him, Lucien and three other capable citizens had to fight their way to stop the downfall of their city.

With the help of the Zane Patriarch a year or two later, whatever threatened Belvar from corruption ended entirely. Yet, Azrael didn't seem very confident in leaving a single noble house alone to rule his beloved city. Therefore, he created the "Underworld" to oversee the city's more inconspicuous parts of the city that nobles fail to notice. Even if Alphonse and the original guardsman had came back from Cathal, Cagliostro refuses to remove the Underworld for the sake of the city.

The great Litarian adventure

Azrael thought he'd be basking in his fame and love among his own Belvarian people and not many, including himself, paid mind to any of the political affairs among the kingdoms around their small Circle city. He even settled down in a nice home with an odd-looking feline as his precious cat companion that loved his cooking!
He didn't realize the drastic measures outside of their city walls until a young prince and his small party came through his vicinity. Much obliged that he took En and guide him to the entrance of Cathal, but unfortunately he was more compelled to follow them to help the Litarian Prince rise. And so he followed him and experienced a rather excruciating adventure.