This is a fascinating question to consider, because, as the magistrate attempts somehow to counteract the brutality of Colonel Joll through his care of the woman that he has crippled and tortured, the magistrate learns a valuable lesson about power and its abuse. The magistrate atempts to care for her in a way that quickly becomes almost ritualistic, as every night he goes through the same process of washing her, drying her body, massaging her feet and ankles and then anointing her body with almond oil. At surface level, this is of course the complete opposite of Joll's brutal violation of her physical health. However, the magistrate is forced into realising that actually there is a smilarity between their two sets of actions that he cannot ignore, as each uses power to entrap the girl. Consider what the magistrate says about this similarity:
The girl lies in my bed, but there is no good reason why it should be a bed. I behave in some ways like a lover—I undress her, I bathe her, I stroke her, I sleep beside her—but I might equally well tie her to a chair and beat her, it would be no less intimate.
The fact that the magistrate is never able to see the girl as a whole person and never refers to her by her name therefore indicates the truth of this view. Although, ostensibly, his motives are so different, he finds that he is actually very similar to Colonel Joll in the way that he uses and abuses power and treats her as an object. The lack of a name cements this view.