I have been making a few different characters and so far, there has been no problem with naming them. Usually I end up with something like, "that name is already taken" then have to spend time thinking up a new one.
Yep, you can have characters with the same name as someone else. Names are connected to one's account.
So, if you and I both made a character named Billy, you would be Billy@BladeParker, I would be Billy@Kamui.