This is an order of the King’s Guard, those charged with protecting the castle, the king, and any holdings. The King’s Guard also guards prisioners of the crown and dabbles in special missions. The Red Hand are the elites of the prisioner guards. While they are competent fighters, that is not their eliteness. They are masters of pain and inquisition. They are the torturers that other torturers speak about in hushed awed whispers. They are the boogieman that every possible rebel fears. They are the masters of the craft, applying careful skills and harsh training to achieve the ends desired.
The Order’s name is actually “unofficial”, as is the order itself. There is no order of the Red Hand on any of the rolls. The name came from the blood soaked handprints on their tunics (an occupational hazard). Those who were properly trained often marked themselves to show their status. Over the last century or two, it has become an official unofficial grouping.