Lords of Kobol, hear my prayer...

I honestly think that in this particular instance Occam's razor comes into play and the answer is as you said the writers simply didn't think ahead :(

However the most logical in text explanation I can offer is as follows. We know from the words of Anna herself and the manner she was treated by Castiel and Uriel that for an angel to do what she did i.e. rip out her grace and fall was unthinkable. It was the ultimate form of blasphemy and completely went against the will of God, which for such a soldier like society was pretty much unthinkable (with the exception of Lucifer and other rebels of course, but I'm referring to 'orthodox' angels.

Therefore the name thing could probably be as simple as a sign of snobbery from Uriel and Castiel particularly Uriah! She had dared to fall low enough to become a human and therefore she was no longer worthy of her angelic name and should be referred to by the 'lowly' human name she was given instead, snobbery at its absolute best basically.

Of course as I admit earlier this is pure fanwank and there is no proper proof within the text to support this, but without relying on real life considerations I think it's the explanation that works best? Although I wouldn't blame you for thinking it sounds like a pile of crap since like I said its just random fanwank rationalizing lol.