If Batman is Bruce Wayne why doesn't he introduce himself as Bruce Wayne?
Reasons Batman isn't Bruce Wayne
Batman lives in a cave...the Bat cave, Bruce Wayne lives in a mansion...Wayne Manner
Batman drives the Batmobile, Bruce Wayne drives some fancy car not shaped like a bat.
When Batman throws a boomarang is a Batarang, If Bruce Wayne does it...it's still a boomarang.
You call Batman with a light in the sky shaped like a bat, You call Bruce Wayne on his Boost Mobile Phone....
Thus I have proven that Batman cannot be Bruce Wayne...Although i do have reason to believe Bruce Wayne is Batman, but don't tell anyone.