Block number while using FaceTime

Someone once asked:

"Is there a way that I can block my phone number or email address while calling someone over FaceTime. I know if you call someone you can use *67 to hide your number but that does not work for FaceTime. I work in a physician's office and we are trying to figure out if we can block our number while we FaceTime our patients."

The answer was negative.

Now that using personal phones for work related items has become increasingly common due to people working from home, or doing virtual appointments, is this something Apple intends to address?

Once people have our numbers I am being contacted at all hours by clients who have no boundaries. Everyone has the expectation of immediate responses and if they don't get it, obsessively text and or call. By addressing this issue, Apple could help put those boundaries back in place.