How to Make your own card more private
Create a “me” card
Go to Contacts > Preferences, and select vCard. Check Enable private me card. At the top of All Contacts, select your card, and click Edit. In the Share column, turn off items that you don’t want included when exporting.
Copy and paste
The private “me” card is a Mac-only feature. A workaround to get a private card on iOS is to make a duplicate of your existing card and then adjust its details. To get started, select your card, and copy and paste it.
Use on iOS
In the copy of your card, delete the fields or elements you don’t want to share with others. Consider differentiating it from your full card with a specific photo, so you don’t accidentally send out the wrong one.