Which region of your brainstem plays a role in arousing you to a state of alertness when someone nearby mentions your name?

Reticular formation

Explanation:

An ancient structural component of the human brain stem, Reticular formations (RFs) comprise several groups of nuclei distributed throughout the brain. In reference to structure, RFs are a net-like arrangement of multi-polar neurons, in a densely interwoven group of fibers. These don't have clearly defined borders, and extend from the midbrain to make up the brainstem's core.

Brainstem RFs are connected to the cerebral cortex and hypothalamus - it mediates sensory functions such as touch, vision and hearing. As these also continue into the hypothalamus, they play a role in arousing the body into wakefulness or an alert state.