Copy value of Primary Contact into a custom field

Summary:

On the Case Management landing page, the Primary Contact and Primary Contact: Name columns are not showing any values, even though a Primary Contact has been assigned to the Case.

We have created a custom field (PrimaryContactName_c), which we would like to retrieve and display the value in the delivered PrimaryContactPartyName field. We will then expose the custom field in the table.

How can we default the custom field value to populate the value from the PrimaryContactPartyName field?

Is this accomplished through a Groovy script on the custom field in Application Composer? What should the script be?