Diablo – Changing your character name

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.

You can change skills whenever you want, but there are currently two penalties:

There's a small cool-down in which you won't be able to use the new skill, which makes swapping skills frequently in combat disadvantageous...

...And swapping skills will cause you to lose the "Nephalem Valor" buff that characters over level 60 get from killing elite monsters, which increases your magic find, causes boss monsters to drop additional items, and, since paragon levels were added in patch 1.0.4, also gives bonus experience.

See also the question on Nephalem Valor