For the Stoics, the soul has parts only in a loose sense — they were monists about the soul where Plato was a trichotomist — but they reserved a specific name for the highest function: hēgemonikon, the ruling or commanding part. It is the rational, deliberative, evaluative centre. It is where impressions arrive, where assent is granted or withheld, where intentions are formed.
Marcus Aurelius returns to the hēgemonikon constantly. The work of Stoic practice, as he formulates it, is the work of keeping the ruling faculty in good order — not letting it be commandeered by impressions, not letting it be inflamed by the body, not letting it grow careless or proud. Hadot's The Inner Citadel gives the term its best-known modern gloss — the fortress within, the part of the self that cannot be reached by external force.
A subtle point. The hēgemonikon is not the same as the will in the modern volitional sense. It is closer to the rational faculty as a whole, including its deliberative and evaluative functions. Sunkatathesis (assent) is the act of the hēgemonikon. In Epictetus, prohairesis — the moral choosing self — overlaps closely with the hēgemonikon, though the terms have different histories. The two overlap but are not identical.
The practical implication: every Stoic exercise — the dichotomy of control, the view from above, the evening review, prosochē — is ultimately an exercise of the hēgemonikon working on itself. The ruling faculty is the only thing that can examine itself. So it is also the only thing that can improve.
Marcus Aurelius, Meditations 5.11, 7.16, passim