Set HidePatronName to show, and on the Holds Queue the patron's name and phone number display. If you set it to Don't Show, it hides the phone number and name, only displaying the card number. The decision to show phone number in the holds queue should not be dependent on not showing the patron name. Perhaps a system preference to determine what info should be viewed?
I think HidePatronName was thought to be a privacy preference - hiding patron identifying information from places where people with no borrowers permission might work or staff from other branches. In that line of thinking hiding the telephone number as well makes sense to me, even if it doesn't quite fit the pref name.
I agree with Katrin.