I understand that you get a number for your online identity. But what about this 'Wii Username' is that just what you liked to be called or is it a registered username?
Buy BWii Thread
It's just what you like to be called. In the Wii it is the "console nickname" option, but when people add you as a friend, it doesn't have to match. This was addressed in the FAQ sticky thread.
... but what do I know?...
Not currently accepting friend adds.