Core now supports custom fields to hide Emails or Names. This will limit who can see sensitive information. This documents shows you how to active this feature.
1- Edit or make a new Select One or Select Multiple Field.
2- Make sure the mark next to check next to Use hub users as option is marked.
3- Click on the drop down box.
4- Click on Name to only show names and click on email to only show email.
5- Save your changes by clicking on the save button in the bottom right corner.
This is what you will see for Names:
This is what you will see for Emails: