Is the eternity of the people of Paradise and Hell a requirement of God’s Most Beautiful Names and Attributes? And do the implications of these Attributes necessitate the existence of another creation in whom the effects and implications of these Names and Attributes become manifest, or is this related to God’s voluntary active attributes, or is the possibility of another creation among the unseen matters?

The premise of the questioner is correct, in that the actions of the Lord emanate from His Names and Attributes, and the actions of creatures emanate from their own actions. Allah is perfect in His Essence and Attributes, and thus He acted, and the creature acted and thus became complete. The non-existence of something is not a defect for Allah unless its non-existence is possible and its existence is better than its non-existence. As for the eternity of the inhabitants of Paradise and Hell, it is a requirement of Allah's Names of Majesty and His Attributes. Allah's Attributes necessitated the existence of sin, retribution, richness, good, and evil. Divine decree (Qada') and destiny (Qadar) are the relation of creatures to the Attributes of the Creator. Allah does not do anything except what His Names and Attributes require. As for unseen matters (al-ghaybiyyat), nothing can be asserted definitively regarding them except with evidence from the texts of revelation.