If this feature is standardized and built in it could be paired with a token like a yubikey which is on users keychain and authenticated even if they were using someone else's phone.
All these details can be completely opaque to the user who just needs to see a blue check by calls made with a device verifiably logged in as name@provider and a red exclamation beside calls made with no info at all.
Think fake kidnapping scams, industrial espionage, recent attacks involved in pretending to be in HR to redirect corp transfers to attacker.
Just a little doubt is liable to blow up such scams.
Remember the standard tech bait-and-switch: if this feature is built in, it'll not be good enough to function for purposes you describe, but it will be good enough to track you by your voice for advertising purposes.