Copy wires with group must retain the net name, as Copy Wires without group.
EAGLE Help : "If you copy wires or polygons, belonging to a signal, the copy will belong to the same signal."
Currently, When I copy a group of wires, the duplicated nets are renamed by eagle and I have to rename manually one by one each wire with the original net name. The same for copying a group of vias.
Wasted time :o(