You can rename the custom fields used by the Risk Register server version. The application refers to those fields by their internal IDs, not their names. Updates to the application will not cause custom fields to be re-created. For more information, see here: https://confluence.atlassian.com/adminjiracloud/edit-or-delete-a-custom-field-991923815.html.
It is not possible to change the field names for the cloud version.