When introducing yourself, is it more proper to say "Ich bin Anna" or "Ich heiße Anna"?
It's a bit of a matter of preference.
Do you feel that "Anna" is your identity, and so "I am Anna" is best? Or do you think that "Anna" is just a name, a label for you, but doesn't define you as such, and so "My name is Anna" is best?*
Might also be regional; ich bin Anna (or the even more colloquial ich bin die Anna / ich bin d' Anna / ich bin 's Anna) seems more common in the south to me, ich heiße Anna more general.
Mizinamo, I like the new voice recordings. Are the readings done by real people or a TTS system? Some of the accents remind me of the South around Baden-Württemberg. Do they sound that way to you, as well? (I haven't been doing German for a while, so what's new for me might have been around for a little while.)
I haven't been doing the German course for months now; I'm focussing on Spanish at the moment when I'm learning, though I still respond to comments on German sentence discussions when I get a notification. So I haven't heard the new voices on the German course and can't comment on them. I assume that stories use speakers and sentences use TTS.