What theory claims that nature exhibits a purpose, end, or goal; i. e., events in the world are directed to the fulfillment of some goal, thus there is a purposeful, goal-oriented structure attributed to the universe?

Teleology

Explanation:

Teleology is derived from Greek words telos - purpose - and logos - study, knowledge, explanation - and means exactly that - the theory of idea where the explanation is in purpose.

This means theory which says everything is happening with a reason and purpose, to fulfill some function or goal.

Aristotle is one of the first and most celebrated philosophers who gave the base of teleology, explaining how anything and everything has a final cause and formal cause, even in nature - acorn has a goal of becoming an oak tree and continuing it's the line.

Philosophers who used the ideas and theories of teleology are Immanuel Kant, Georg Wilhelm Friedrich Hegel, David Hume, and William Paley.