Unfortunately, this isn't an option. Badge earners can choose to make badges public or private and can also make the decision to share badges to social media (or not). Earners have full access to visibility controls and must take action to share badges if desired.
A badge is a digital representation of an earned credential/certification and for verification purposes. Earners are not able to change the information stored within a badge. That information is controlled by the issuer. The earners full name is used and displayed for verification purposes. Email addresses are never displayed and, earners are in control of how much is public or private, through the Acclaim profile Account Settings.
At this time we do not have the ability to allow earners to display badge but not the issued to name. If the badge is public, the name would be displayed as part of the badge details. When a badge is set to private, only the earner would see those details.