https://stackoverflow.com/a/52525587/12716363
They said:
iOS and Android - The SMS messages draw the app's name from the App Store / Play Store. One an app is published, the correct name should start appearing. There may be a small delay (a week or two at most).
My app has lived a few months but our SMS messages are still: Your firebase app verification code is ...
I tried setting Firebase -> Project settings -> Environment type to Production
and changing Public-facing name still does not work.