The problem is not the Group names (you can make these different by setting extra options on export), but the material names, which can't be altered by Python internally.

AFAIK the only way to change material names is to use a text editor (or a program) on the OBJ file and the CR2/PP2/PZ3.

This is a non-starter, as all your MAT poses would stop working for the items with renamed materials.

Your only hope might be to see if exporting the OBJ from DAZ Studio is any better.