"It's the name I was given." The Bat said it as if there were no other choice. Zoe knew the history of the name, but she saw no reason to share the history. Giving the history also seemed like a way to open up the name, herself, and her loved ones to trouble. The boy would claim to be trustworthy, but the last time she'd seen him Rufio had not acted like he could control himself. He had to learn how to handle those emotions still.
"I suppose you could say I do." They kept pulling the thug out, and soon they'd have him to the door. "The police are useful, but there are times that some of us must take the law into our own hands." The way the Bat said 'us' suggested that Rufio was not one of them. Then again, this Bat didn't have nor planned to ever have a sidekick. There was no Robin, and would be none.
"You'll have to rework your traps. Don't let them get so far inside. They could use this against you too. Call the police to come get you. Hurting the authorities, while fun at times, isn't always the best." The Bat didn't usually talk this much, but the boy needed to know the dangers that could await him.