Can businesses and other entities identify a user based on a phone number they have provided? (U.S.)

By "identify", I mean to access personally identifying information associated with the subscriber of the given phone number. It appears that PayPal does this, since they allow a phone number to be used to verify full name (and possibly address); they verify that the full name provided (and possibly address, I’ve forgotten) matches the full name associated with the phone number that the user provides for verification.

I assume this information is not entirely public. Which entities are allowed to access it? Is there a central registry maintained by the service providers? Can anyone access it?

I am curious in particular whether "lower-level businesses or websites" (relative to PayPal, which presumably has some kind of legal obligation/status with regards to identity verification) which a user might provide their phone number to, such as dating apps, messaging apps, social media, etc, are able to access this information. (personally identifying subscriber information)