Sorry, but how in the hell did they figure out who he is? With nothing to go off but a description and some else's name? Even if they had spies in every city in the country, he's one homeless orphan. There are maybe 2 dozen people still living who even know his name, and none of them would rat him out. I can overlook a lot in stories like this, but them discovering his identity within days of starting their investigation is absolutely ridiculous.
Its been awhile, so IDK if this question is still valid or not, but I'll at least take the stance on the story-writing side. 'There are maybe 2 dozen people still living who even know his name' this is false, you need to remember the reason why he had to run away from the slum in the first place, its due to conflict from the other gangs. And wouldn't you know, that took care of the loophole of 'none of them would rat him out' immediately, since these opposite gang members are more than likely would spill out all shit about him as much as they could if given a compensation. Not to mention, he has blue eyes and blond hair, its too eye-catching and even the story so far have always try to emphasize that point in any given chance. Think, in the slums where people can even kill just to survive a day, how much thing inside there can entertain them? His previous workplace is exactly one of that (In case you forgot, its a whorehouse). So anyone that can afford a dozen of silver coins to some gold coins would've visited his workplace already, you would think its logical they'd remember a candle boy who have blue eyes and blond hair. Even if the investigation start with 'blue eyes and blond hair', it wouldn't take long until they found someone who've heard of his name being mentioned before long. Again, these people are from the slums, its easy money for them to speak and spill information, even if it ruined someone else's life. But I kind of agree about the last point, there's no indication of how far he has travelled, so the investigation making that high of a result in just a few days span was a bit off unless the slums is close to where they're currently stationed (which I don't think it is, thus why I agree to that point).