For those of you who have not purchased Stacraft 2 yet, here is some information about creating your Starcraft 2 account that everyone should know:
(2013 Update: It is now possible to change your name for a fee through battle.net.)
1. You are stuck with the name you pick forever. As of right now, you are not allowed to change your name, so make sure you pick something you will want to stick with for a long time. When it asks for your "character profile", it is asking you for a permanent battle.net name which you will be playing online with. Blizzard has not announced any plans to implement a feature to change your name, and if they do it will probably require a fee.2. You cannot rename your account, you cannot delete your account, and you cannot create more than one account. You also cannot delete your account and then create a new one. The one way to get a new name is to buy a new copy of Stacraft 2.
3. Names are not unique because what separates you is your character code, so you can have pretty much any name you want! (But once again, I can't stress this enough, you cannot change your name) If you want to play with a friend, you will need to tell them your name and your character code, that way you will not get mixed up with people who chose the same name as yours.
So in conclusion, go ahead and pick a name you want, but just remember you will be stuck with it. The good thing though is you can have any name you want, since once again, they are not unique.
Remember that when it asks you for a name, it may seem like the name is just for the single player campaign, but it is really the name you will be stuck with for battle.net as well.