A RDF Graph in the Virtuoso Quad Store can be renamed without copying each assertion from the old graph to the new graph using a SQL statement, this being what the Conductor "rename" option does, which is:

UPDATE DB.DBA.RDF_QUAD TABLE OPTION (index RDF_QUAD_GS)
   SET g = iri_to_id ('new')
 WHERE g = iri_to_id ('old', 0);

Note: this operation must be run in row-autocommit mode i.e. log_enable (3), and then restore back to the default logging mode of 1.

For Virtuoso Graph Groups two tables need to be updated:

UPDATE DB.DBA.RDF_GRAPH_GROUP_MEMBER
   SET RGGM_GROUP_IID = iri_to_id ('new')
 WHERE RGGM_GROUP_IID = iri_to_id (old)

and

UPDATE DB.DBA.RDF_GRAPH_GROUP
   SET RGG_IID = iri_to_id ('new') , RGG_IRI = 'new'
 WHERE RGG_IRI = 'old'