If you expect to need to edit this information then I would setup an app-specific case property. You could default this to the creating user in the form that creates the case, but then you could also have a "reassignment' form that changes it to someone else, and you could use the case importer to set it in bulk.
This would require modifying your app. Alternatively, you could just add this property only if the contact changes, and then train your staff to check that property first and fallback to the username if not set. That could be rolled out without app changes.