Hello @Tom Thompson ,

Once the group name has been changed, all the reference fields holding that group will be updated to the new name & this is an expected behavior from ServiceNow. 

However, to fulfill your requirement you can create a new string field to copy the old group name once the request has been submitted so that the old group name is visible even though the reference field got updated.

Please let us know if this fulfills your requirements. I can provide you with a script to achieve it.

Please mark it as "Accept as Solution" and " Helpful. if this solution helped you.

Thanks & Regards,
Madhan Somesh.