From Diablo Wiki
The BattleTag is a player-created name that serves as your Battle.net title. It is used in all Blizzard games, as well as on their forums and community websites. Players create a name of up to 12 characters, and this becomes their official title on Battle.net. Your BattleTag is what other players see on your Diablo III characters, and what appears on their Friends List.
- See the official Battle Tag FAQ for additional details.
The BattleTag was introduced in December 2011.
The BattleTag system is an evolution from the Real ID system Blizzard attempted to introduce in early 2011, until massive fan outcry over the privacy issues forced Blizzard to rework it.
Changing Your BattleTag
In response to fan requests, Blizzard enabled a BattleTag name change in April 2012. They said it was one time only per account, and urged fans to choose wisely.
Another one-time amnesty was rolled out a month later, as fans found how important BattleTags were in game (they show the vast majority of the time when online, with specific character names seldom displayed) and petitioned for another change opportunity. They got it, with an announcement on May 17th just two days after Diablo III's release. 
To help address these concerns, we've done a one-time refresh of the free BattleTag name change feature on all Battle.net accounts, so that everyone once again has one free BattleTag name change to use at their discretion.This means that if you already used your original free change, you will now have another opportunity to change your BattleTag nickname. If you did not use your free BattleTag name change or have not yet created a BattleTag, you will still only be able to change your BattleTag once for free.
While most players liked the functions and convenience of one BattleTag, there were many complaints about the lack of character customization or identity. BattleTags display always in-game, so whether your friend is playing his Wizard, Barbarian, Monk, etc, all you ever see is the same BattleTag.
After numerous complaints about this during the Beta test, Bashiok offered a ray of hope by saying that the system was under review and the final game should offer more options for character name display.
That turned out not to be the case, as a month later Blizzard announced no changes to the system.
Lylirra, can we get some clarification on where character names show up vs. Battletag?Sure thing! When Diablo III launches, your character name will be visible to you in a variety of locations including the character selection screen and game menu. For other players, your character’s name will only appear within your player profile, as hover text the friends list, and when your character participates in quest dialog. In every other context, your BattleTag will be shown.
After the above news, leading fansite Diablo.IncGamers.com ran a poll to get to the bottom of fan opinion. The results showed a clear preference for character names over BattleTags:
Do you prefer to see Character Names or BattleTags?
Total Voters: 5,646
- 1) Character name should display in-game and chat. (43%, 2,436 Votes)
- 3) Give players the option of which to display and view. (32%, 1,787 Votes)
- 2) BattleTag should display in-game and chat. (15%, 858 Votes)
- 4) Don't care/no opinion. (10%, 576 Votes)
The BattleTag FAQ answers this question neatly enough.
BattleTag Name Limitations
Since the BattleTag system debuted during the Diablo 3 Beta, D3 beta testers were among the first people to use the system. Most fans liked the design and concept, but quite a few ran into problems when trying to create their BattleTag, due to the strict naming policy. It's very easy to hit upon a name that's not allowed, and as there is no explanation offered, players just have to keep trying different names until they find one that's permitted.
Blizzard's support page can be seen here; it lists the dozens of categories of names that are not permitted, which include many vague umbrella terms, including the following:
- Have any racial/ethnic connotations.
- Are inappropriate references to human anatomy or bodily functions.
- Insultingly refer to other characters, players, Blizzard employees, or groups of people, be they in the game or external.
- The names of any customer support representative or employee of Blizzard Entertainment (Both real names and aliases.)
- Are mildly inappropriate references to human anatomy or bodily functions.
- Are references to illegal drugs or activities.
- Have neutral or positive racial/ethnic/national connotations.
- Are otherwise considered inappropriate for the game world.
- Are trademarked/licensed by a company or an individual.
Blizzard obviously had to stake out a vast area of forbidden names, to give them wiggle room in the future. That said, the banned terms are so extensive and vague that potentially anything could be disallowed. After all, no one could possibly know the real names and aliases of every single Blizzard employee, much less every obscene slang word in every language on Earth, or every trademarked company name.
Fans can only hope that Blizzard employs some discretion in assembling their banned name list, and that there's some built in mechanism to automatically switch friends over to a new name, should one in use be deemed inappropriate.