You can view the Box Names under the Group box that the group contains. The Group contents will list all the Box Names that the Group contains. If you want to see the Box Names without having them listed under a Group name, ungroup the boxes and then do the deconstruct.

When objects are grouped in QuarkXPress, the group itself can be given a unique Box Name. The group is then identified by the Name assigned to it. If you have grouped any named boxes and assigned a Name to the Group, the Group box name will override the individual Box Names when the layout is deconstructed. In the output you will see the information listed under the Group name.