What part of the cerebral cortex is responsible for personality, the creation of an awareness of self, and the ability to recognize appropriate behavior?

The cerebral Cortex (The prefrontal cortex)

Explanation: The cerebral cortex is the outer surface of the cerebral hemispheres, the furrowed outer layer that contains the gray matter in the cerebrum of the brain that is associated with higher brain functions.

It is the highest level of the brain,

The cerebral cortex have about 20 billion neurons which aids it to carry out the highest levels of mental functioning like as voluntary movement, coordination of sensory information, learning and memory, the creation and awareness of self and the ability to behave appropriately.