Seems like most of everything else has been addressed already but I wanted to add here that Friend#2244 is the Battle Tag. Adding someone via this method they will only see you as Friend. Adding someone with your RealID (your email) will show you as Friend (Firstname Lastname). Avoid RealID and only add people with your Battle Tag if you don’t want people seeing your name.
If you ever decide you want account wide friends, that is