Your Starcraft 2 character will be your online name yes. When people ask to be your friend, you can tell them your Starcraft 2 name or B.net name. Real ID friends on Battle.net can see each other's full profiles, including real-life names, real-life profile information, and all of their characters across all Battle.net games.
With starcraft 2 name, you will immediately start seeing that character in your friends list, but you will not be able to access real-life names, real-life profile information, or any other characters he or she might play. Other players are not notified if you add their characters to your friends list in this fashion.