Strangely enough there used to be which is why to this day my mobile has a confidential, unlisted number.
Sometime around 1993 to 1995 I bought my first mobile. The telephone company had this weird idea of publishing a paper white pages directory of mobile numbers and as in their minds mobiles were only for business use back then wanted me to pay to be in this directory.
When I said I wasn't prepared to pay the nice lady at the phone company call centre discovered that the only way to drop me from this directory was to make my phone confidential & unlisted where it stays to this day.
This means caller-id doesn't work on voice calls, but does show up on text messages. I suppose one day there could be a negative to this but until then I can't be bothered spending an hour on hold to have it done.
BTW I don't have the same phone, nor exactly the same number but somehow the setting always transfers