Manage phone numbers and names in "Bury Contacts" not "Contacts" to not disclose this personal data to third parties.
Features
Incoming calls are identified by the phone number. Known names are displayed on the call and in the recent calls log. Alternatively, call blocking is possible. "Bury Contacts" can be searched and dialed. All data is stored in a single large text field that is only stored on your iPhone. Use copy&paste to import/export and backup/restore.
Background
Bury Contacts was developed by an entrepreneur accountable for the protection of the rights of individuals under Chapter 3 of the European Union General Data Protection Regulation. Some of the rights, such as the "right to be forgotten" (art. 17), can not be exercised as soon as data is passed on to inappropriate third parties. However, the scope of the EU GDPR does not apply to "personal or family activities" (art. 2c). The idea is to use "Contacts" with third-party apps such as messengers for private fun and "Bury Contacts" for business purposes.
Limitations
Bury Contacts is only a makeshift and not a replacement for "Contacts". It not even comes close to. You don't get much more beyond a label on a number for an incoming phone call. On iPhone display only. Not on Bluetooth or otherwise connected devices. No audio call announcement. No Siri. Do not expect great enhancements, intensive compatibility testing or great customer support. Maintenance will likely be discontinued once a better solution exists.