Accounts here have both a user name and a display name. As you might guess from the name, a display name is what people see, but not the actual name of your account. I had my display name changed long ago to remove my underscores, but I still have to use them to sign in since that's my original user name. Mods and admins can change a user's display name, which is how Khushrenada was able to swap people's names a bit ago to play pranks, but still allowed them to sign in using their user names. I don't think it's possible to change the actual user name, though I could be wrong.
I'm pretty sure the software would allow both display names and custom titles to be user-changeable, but those options have been disabled to allow only mods and above. I can understand why they wouldn't want users changing display names on a whim, but users not being able to change their own titles has always struck me as an odd decision.