I have settled that to my satisfaction by having Amy Milton dream that her unborn daughter's name was Anael and Amy waking up and deciding it sounded pretty but wasn't a real name so she named her daughter Anna Elizabeth Milton.

As for why the angels all call her Anna, even 5x13!Uriel who doesn't yet have any idea that Anna was/will be born human, I don't know. Maybe angels don't interact with language the same way humans do, so they're drawing descriptive terms from the minds of the listeners so as to be sure they're communicating in terms the listeners understand? And Castiel's Babelfish doesn't work right, which is why Zachariah can do pop culture references and Castiel not so much.