N1b
I changed my phone and contacts slightly to prevent my caller ID from being sent out on calls except to people I trust, and who don't install snoopy apps that will leak collected caller ID and name to surveillance capitalists.
I'm using the default AOSP phone app for these instructions.
Proceed: Phone > 3 "." menu > Settings > Calling accounts > (name of cell service provider) > Additional settings > Caller ID
Select "Hide number"
Exit.
Your caller ID will be blocked (not sent) by default now. Toll free 1-8xx and some other numbers can still get your calling number by other methods (e.g. via Automatic Number Identification). I discovered that my city's 311 number received calling number even if blocked.
Test that caller ID blocking is working by dialing a number you are willing to share your caller ID with. Confirm your actual Number and name is not displayed when the destination rings.
Now go into phone contacts (address book).
Add "*31#" before the numbers you wish to send caller ID to. This prefix will cancel the default caller ID blocking default you just set for each call with that contact. Save the updated numbers for the contracts.
Test by calling a number you want to send caller ID to and verifying that it is displayed.
If you also display caller ID for calls from that contact, you need to add another contact number for them of type "other" which has the original, plain number without the prefix.
Test by having that number call you and verify it is displayed.
This is an ugly hack but it works for me. The "show caller ID" prefix "*31#" must be tested with your mobile service provider as it may not work with all. Some phone apps may be more sophisticated and able to inject the prefix into outbound dialing. I have not researched this. I have very few numbers that I call and want to send caller ID to, so this config was an easy way for me to enhance my privacy when I call local businesses, government offices, and other people etc.
This caller ID selective unblocking prefix setup might work on any phone which can enable default caller ID blocking, not just GrapheneOS on Pixel. It has been tested and also works on an iphone.