In real life we create characters, building them up from what we see and hear. Meeting someone online or by phone, we build their personality from their words. This tendency can be so strong that people involved in Turing testing sometimes can't believe that they've been interacting with a mere computer. The effect is even stronger when voices and images rather than text is involved. Animals have personalities, even plants and objects can become possessed. The characters we thus create can seem unified, independent of any particular physical act, leading people to talk of disembodied personalities, spirits and souls, of afterlife and Gods. On top of that we create self-images; we are self-conscious, and assume that others are too.
Once we've created characters, they can surprize us - "It's not like her to do that" we might say, or "It's so out of character". Some people have "more" character than others, they're "larger than life". Alzheimers sufferers seem to gradually lose their character, their self. People with severe autism and robotic behaviour are sometimes credited with having less character.
Writers are in the game of creating believable characters. Sometimes during the writing of a story they are totally immersed in a character (if the character's unpleasant, depressed, etc, this may have consequences). Actors bring characters to life even more strongly than readers do, telling the playwright when their character wouldn't say the scripted words, replacing them with their own.
This character-creating ability presumably evolved to help predict others' actions (self-consciousness perhaps being a by-product). It's rather complex and varied. We often present a different self-image depending on context (extrovert with friends and quiet with parents, for example). A few people (very few) develop multiple personalities each unaware of the others. More commonly, people experience depersonalisation, seeing others as actors, as dolls. They even see themselves as artificial. Depersonalisation (often associated with depression) can be viewed as a hitch in the character-creation faculty, the inability to see the ghost in the machine. Autism is described by some people as "person-blindness".
Depersonalisation can lead to derealisation where the world seems comprised of stage scenery or part of "The Matrix". The way we create an internal representation of the world is complex too, even more so if Quantum Mechanical notions of what is "really there" are included, so it's no wonder that our world-creating facility, like our characterising facility, breaks down sometimes. Agnosia is the term used to describe the inability to process sensory information, to identify objects ("At first I saw the front part. It looked like a fountain pen. Then it looked like a knife, it was so sharp but I thought it couldn't be a knife, it was green. Then I saw the spokes").
When we look at someone face on, then they turn their head to the side, we know it's the same person. When a quiet co-worker becomes an extrovert scene-stealer at late-night clubs, we know it's the same person. Creating a character from these parts requires memory, which is why there's a dementia connection. Without memory, our inability to create characters can lead to an inability to predict behaviours, causing anxiety and agitation.
Such is the strength of our character-creating instinct that writers don't usually have a hard time convincing the readers that the characters are real (indeed, fact can be stranger than fiction). Easiest is to copy a character (real or fictional) who people already believe in. Writers can make their work more effective by understanding how people create worlds, memories and characters, and how that process can vary. People with dementia often retain their habits and preferences (for particular colours of clothes, flavour of ice-cream, etc). Is that kind of detail sufficient in a novel to establish a character? It might be, especially for minor characters. A fully rounded character's behaviour needs to be reasonably predictable without being deterministic. It helps if they exhibit similar traits in various situations. People are a mix of the predictable and the surprising. The predictable features aid identification and empathy, making surprises possible. E.M. Forster wrote that "the test of a round character is whether it is capable of surprising in a convincing way."
One can analyse the characters in a story as if they were people, or one can "depersonalize", viewing them as constructs and analysing how the writer tried to supply the building blocks. Writers might try to depict non-standard processing. There are several examples of novels where the main character's autistic (e.g. "The Curious Incident of the Dog in the Night-Time" by Mark Haddon). Sartre's "La Nausée" depicts bouts of Derealisation. As well as Existentialism, some other literary movements encourage such depictions. Some "Nouvelle Roman" texts focus on pre-processed perceptions - the reader needs to memorise the perceptions in order to create characters and objects, because the authors don't always do the integrating.
In The Fractured Self: Postmodernism and Depersonalization Disorder, Conor Michael Dawson points out that "Postmodernists began to reject identity as a psychologically whole entity, heightening Eliot’s “process of depersonalization” to morbid extremes". I think Eliot meant by "depersonalization" something more like "objectivity" or "detachment". The texts Dawson offers as examples are "In the Lake of the Woods" (Tim O’Brien), "The Vietnam in Me" (Tim O’Brien), "Fight Club" (C. Palahniuk) and "Black Swan" (a film by Darren Aronofsky). Elsewhere, Bernice Reuben's "A Five Year Sentence" is suggested. I've read/seen none of them.