For example, terms like "the patient," "our Father below," and Screwtape's affectionate language towards Wormwood. It actually strikes me as oddly similar to the "doublethink" used in George Orwell's 1984. In the latter case, however, the purpose is obvious — manipulation, control, and deception of the general populace and especially the party members. But in The Screwtape Letters, we have one literal demon writing to another, (and presumably an attempt at portraying a demon specifically as understood in Christian theology, considering Lewis was a strong Christian, as well as the nature of the work itself). And for the most part, Screwtape doesn't try to hide his true nature or intentions from Wormwood. He openly admits and explains the "bring food or be food" attitude of hell and their delight in tormenting souls they "win". So what's the point of using misleading euphemisms like "the patient"?
I'd say it was perhaps that even someone as evil as Screwtape has some desire to think he's really the good guy on some level, on the right side of things. And if he were human, or a more generic type of "demon", as often show up in general fantasy works, that would make sense. But Lewis was specifically trying to portray some version of a demon as understood in Christian theology, yes?
Maybe my confusion is because I'm Catholic and trying to understand the theological implications of the text through that lens, while Lewis was Anglican. In Catholicism, the belief is that the angels who joined Lucifer in rebelling against God knew exactly what they were doing and the eternal consequences. That is, unlike humans, who get many chances to repent, angels had one opportunity to choose to accept or reject God because they had full knowledge and understanding of exactly what that choice would mean in a way we don't. Also, unlike us, angels and demons exist outside of time and therefore cannot change.
Doing some Googling on the topic, this seems to also be the mainstream understanding of most Protestants as well. Given that, it seems strange that a character meant to be a portrayal of a such a demon, as understood in Christianity, would bother with attempts to mask his true nature from another demon. Was Lewis's understanding of the topic different from the current mainstream Christian understanding? Or perhaps even the general understanding of the topic in many Christian denominations was a bit different in the 1940's?
I do know that, from an out-of-universe perspective, both the language and the portrayal of hell as being run like a corporation was meant to satirize/criticize actual corporations. (Many articles suggest this and it makes sense, though I'm unsure if Lewis himself ever said this was his intention). But is there an in-universe explanation?
