For the past 80 years, Batman's character has evolved into many different incarnations, but one of his major character traits in most modern versions is his one rule: No killing.
While it's convenient for The Dark Knight to follow that type of code because it conveniently keeps his villains alive for further storylines with them, but it also makes him a compelling hero. It's one thing to eliminate crime by killing the criminal, but attempting to eliminate the crime by reforming the criminal is a more honorable way of distributing justice.
Batman detests and is exhausted by his enemies, but he still wants to reform them deep down inside. This is why, according to this fan theory on Reddit, he has another rule along with no killing. That rule is not to call his antagonist by their chosen villainous moniker, but rather their real name.
This characteristic of the Caped Crusader has been prominent in the Rockstar video games like Arkham Asylum and Arkham City, as well as Batman: The Animated Series. Examples include referring to The Penguin as Cobblepot, Two-Face as Harvey Dent (something he also did in The Dark Knight), and Poison Ivy as Dr. Pamela Isley. He still calls The Joker by his nickname, though that's the only known identity he has.
Not only is this a smart strategy by Batman to subconsciously knock his enemies persona down a peg by reminding them of their humble roots, but it's also an attempt at finding the good person deep inside them. His enemies are not born evil, but it is typically thrust upon them due to unfortunate circumstances. Being reminded of their innocent former selves may give Batman a kernel of hope that they will surrender and attempt to rehabilitate themselves.
After all, if Batman is going to stop criminals from committing terrible crimes without killing them, what's the point of doing it if he knows they will eventually figure out a way to break free and do it again? It's a cycle that continues to repeat itself, and the only reason Batman persists is that he still believes he can reform them.
The Dark Knight will use whatever psychological tactic he can against his opponents, even to the point of respectfully acknowledging his enemy by their real name. Every villain in the Batman universe thrives on a larger-than-life persona that's far from their original identity. Each one is such an exaggerated version of themselves that they likely forgot who they were and where they came from, which is why they at least have Batman there to remind them.