I bolton, first off, I’m glad you have embraced the practice of reading scripts and watching movies. It’s absolutely critical in learning the craft of screenwriting IMHO.
Re identity as a theme: I believe that lies at the heart of most every movie, an existential question for key characters, especially Protagonist figures: Who am I?
Young’s appropriation of a character who, as it turns out he killed, is, I think, a way of attempting to deflect his responsibility in that character’s death. By ‘becoming’ another individual, he tries to distance himself from his own actions. The fact he takes on the victim’s name reflects how he knows -subconsciously-he cannot succeed in obliterating the details of his past actions. Ultimately, he *has* to confront the past. Symbolically, his death can be seen as justice meted out by the universe based upon his previous ‘sins,’ specifically killing Winslow.
Re madness: If we step way back from the story and look at it from a mile high viewpoint, my take is that if any of us were to seclude ourselves from our busy lives, after a point, it’s likely we would slip into some sort of ‘madness.’ At the very least question our value systems and priorities. Frankly, The Lighthouse is a great movie to consider given the current state of quarantine related to the COVID-19 pandemic. People cooped up in their houses and apartments is akin to being stranded on an island, and we have a *lot* of time to reflect on who we are, why we are, and how we are.
To your final point, I agree that the movie isn’t about good and evil, so much as it is about the fragile nature of the psyche, the thin veneer of what we do to create a sense of ‘normalcy’ to create a boundary between our daily lives and that ‘madness’ which lies within.
Thanks for your reflections!