It can still be polite, or routine, to ask for someone's name, even if on a badge. It's not unheard of for people to have the wrong name badge or patch, although obviously the expectation for accuracy is different for military name badges over civilian name badges (where sometimes people swap, for fun, or just wear whichever one is available, if they're not allowed to take them home, or choose not to), or just to ask to call people out in a good or bad way.
You might want a first name, too.
It's not socially inconsistent, anyway.
You do seem to be conflating, to an extent, logical inconsistencies with social or personal preference inconsistencies. Something can be logical but socially inappropriate, or illogical yet something some/all people do.