[Charles himself is particular, but he understands that some people would really rather not constantly call him "Assassin". Besides, he's still obscure enough within history that only someone well-read in French history in particular might be able to make the connection.]

That's because a Heroic Spirit sharing their real name would essentially be sharing their strength or weakness along with it. But others are more confident, or simply don't care while they're in an entirely different world.