Choosing a BattleTag, how is it used?

Your Battle Tag is the primary means of identifying yourself on Battle.net in Diablo III. Most people I know use an existing online moniker for their Battle Tag. Your Battle Tag is made unique by adding a hash mark and four digits to the end of your chosen name (i.e. #1234). I don't usually go into the general chat channel, which is where you would see a lot of different names, but I'm sure there's a wide variety of Battle Tags from the extravagant to the mundane, and the silly to the serious.

While your Battle Tag identifies you, there are also character names that identify your characters. For instance, in my friends list I might see MyFriend#1234 (the Battle Tag) was last seen online playing the Demon Hunter, Buffy (the character, and I really wish I had thought of that before) 5 hours ago. That wording isn't exact, but you get the idea. Character names are generally more thematic and extravagant because while visible, they're not used for identifying the player in any fashion.

In general, I usually ignore the character name of my friends as the class and level are better for identifying the character your friends are playing with. For instance, I might tell my brothers I'm playing with my monk, which they know is a lower level character that I've been soloing with, so they know not to join my game.

One more important note: You can only change your Battle Tag once after it's been set. You might also want to look at the Naming Policy.

Your battletag is what most players will see from you. The character name will only be displayed when someone access your profile. You can even name all your characters the same, there's no "character name collision" concept on diablo 3. So for example, if my battletag is 'stoldark', and my character name is 'JoeMonk' other players will see messages about me with my battle tag. For instance: "stoldark was slain" "stoldark found a new waypoint" They will see I am playing with 'JoeMonk' if they see my profile.