Are character names unique in Diablo 3?
Solution 1:
Battle tags are unique, but character names are not necessarily. Remember, the battle tag includes the number, so two people can choose the "same" battle tag but will still be differentiated based on the number afterwards.
Most of the in-game interactions are done via battle tag, not character name. When someone chats, his battle tag (without the numbers) is displayed instead of his character name. Similarly, people's battle tags are shown under their character portraits rather than their character name.
It may get confusing if two people with the same base battle tag join the game.