@Janette - read the FAQ that dwanthny pointed you to above. I'm afraid you can't have it both ways - "not being fussed about whether names are FN LN or LN, FN" and then being surprised when your authors don't sort correctly
You have to pick a scheme, set the tweak properly (if you decide on LN, FN) then use the Manage Authors dialog to cleanup the mish-mash you have currently.
The other thing not mentioned on this thread is setting the sort for Calibre at startup which might be relevant. Go to Preferences -> Tweaks -> Specify columns to sort the booklist by on startup.