This is something Introduced in Apple IOS 12.2
It appers in Flash SMS, which is often used for e.g. One time passcodes.
I have tried to contact Apple support about this, searched for documentation, release notes etc. and it is not documented anywhere. The text is injected into the message, which is an issue. Especially for Messages send containing security information or copyrighted text (a violation of copyright?).
@Apple, You need to address this.
Your text (This sender has not been verified) is injected into the sender text as part of the text. There is not documentation on how to become a verified sender, or how to turn of the feature. Your support centers has no idea on how to help with this issue.