If its yes It doesnt defeat the name of the merciful and Just,first of all,why does it defeat the name of Al Rahman and the just?
Have you forgotten Allah SWT CHOOSES to be merciful as he says in the Quran?
Allah chooses to merciful and Just,but
Allah can be unmerciful and unjust, but that would defeat his own purpose,to be the most merciful most Just,so he stays Merciful and Just.