He hates his past, his guilt that he doesn't want to remember. He avoids the past version of himself, healthy, happy, and a killer. So he throws this part of his character away. This separation is too much that the thrown away past turn into a new, fictional, independent character. A pain in the ass and as disgusting as possible in Trevor's eyes (ugly fingers and laughing, etc...). Trevor doesn't want to remember his past year.
However his subconsciousness has created the past version of him, everywhere, communicating with people he knows, working at the same place, etc. to remind him of something. That hanging-man game, for example, is his subconscious intention to remember and accept his guilt. And when he accepts his guilt and past perhaps can go back to the normal life he had before the accident. To sleep, not accusing people, not washing his hands with bleach, etc.