I've created a new Battle.net account, and I've chosen a new BattleTag. There were no errors indicating that the tag was already in use or anything like that.
However, when I go to Account Management, and look at my BattleTag, there is a hash (#) and a 4-digit number appended to it!
Battletag #1234
What does this mean?
It's a random number that is attached to every BattleTag, no matter whether the actual name is unique or not (the number makes it unique as the combination has to be unique). It's usually hidden though.
It essentially makes your name unique while allowing the readable/name part to be used multiple times. That means, you don't say a friend to add "BattleTag" to their friends list, you tell them to add "BattleTag#1234", because there might be more than one "Battletag" in use. Despite that, in games you'll usually just appear as "BattleTag", unless there's a second player with the exact same BattleTag.
