There's been a lot of wonderful meta about magicians "dehumanising" themselves in order to uphold the system of power, and while this is true, I propose you another concept: instead of acting like it's denying the concept of personhood, the magician system acts like it replaces it.
Changing your own name, ripping you from your family, from your heritage, from your social statues as a commoner, from your friends and your community, all of it is indeed acts as driving force of making magicians symbolically less "human". However, the system does not present it like that. The system presents it like a needed sacrifice to form a new, "better" sense of personhood within your role as magician. They teach that to be valued as a human being, to be regarded as a person, you have to exist within the system and serve its unspoken biases, because otherwise you're none of it. Otherwise you have no name, no job, no purpose, no reason to call you a human. They replace the overall understanding of personhood established in every other society, granted by existing, by loving, by being a human, and make it a condition.
And this creates a very interesting perspective on a relationships and relations of power within the book. Because both Bartimaeus and Nathaniel struggle with regaining their personhood in very similar ways. Both believe that being a person is something to be placed upon you, something someone higher than you has to decide, something you had to pry open from their cold, dead hands. See my post there on briefer explanation.
Nathaniel struggles with proving he's worth being seen as person and regarded as an equal within the higher magician society where every mistake can make you dead. Bartimaeus struggles with being seen as a person and regarded as an equal within the system whose every brick is built on not seeing him as one. And while their struggles are not fully comparable — we have to remember that Nathaniel is on a privileged, opressing side of the line, maybe not as much in a very unique case with Bartimaeus (hence he knows his name, which doesn't balance them completely but makes it more balanced than a typical example of magician & spirit relationship) but within the overall system of magician-ruled society (commoners and spirit slavery), the sentiment which they have towards earning that personhood (described above) is indeed very similar.
The main difference is that Nathaniel sees the turing process of regaining this personhood through the lense of perceiving everyone else outside of his "cast" as less human (both a desperate attempt from his circle as being more human in comparison and the rule he was coerced to believe is the truth), while Bartimaeus sees this process of rejecting the understanding the human definition of what makes a "human" all together and instead relying on his own condense, the existence of his feelings (as much as he likes to deny this), the actions and virtues done by him. He was never supposed to have singularity all together, yet here he is, and he has a very difficult inner dilemma of enjoying being a separate person and being denied this feeling from everyone else around him.
For Bartimaeus being a person is something he was never supposed to have, yet he was forced to be one and now he has to fight to be seen as one, the fight he claims to give up yet never stops fighting it. For Nathaniel being a person is something he was supposed to have from the very start, yet he was denied it and now he has to fight for being seen as one within the new, fake condition he sees as "right".
