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The only way to really do this is to have the caller block their number when calling in (*67). In your call reports, you will usually see your account phone number where the caller's phone number would normally be.

There is no native way to not share the ANI in the call reports/logs. As u/welcome said above, the most you could do is restrict those who have access to company call records via a custom role.

I think it is not possible to hide this info from a Super Admin who has access to the Company Call log.
You could potentially hide it for a user ext. by doing these 2 steps:
1. Use a custom role to remove access to the User call log and Company call log
2. In the admin portal > Users > click on a user > Phone > Incoming call info > select Dialed number instead of Incoming caller ID.

Haven't tested the above btw, but it might just work.