What is the name of the item that supplies the exact or near exact voltage at the required wattage to all of the circuitry inside your computer?

A voltage regulator.

Explanation:

A voltage regulator, controls the output of an alternating current or a direct current (depending on the design), allowing the exact amount of voltage or wattage to be supplied to the computer hardware. This device sometimes uses a simple feed-forward design or may include negative feedback. The two major types of voltage regulator are based on either the electromechanical or electronic components.

The electronic types were based on the arrangement of resistor in series with a diode or series of diodes, and the electromechanical types are based on coiling the sensing wire to make an electromagnet.