What the reader is presented with here in the initial group therapy session over which Nurse Ratched presides is the beginnings of a battle that continues throughout the rest of the novel. Nurse Ratched deliberately calls McMurphy by a name that she has chosen as a symbol of her power and her dominance. She, as the clear leader of the ward, is able to shape the identity of the patients as part of keeping them controlled and under her thumb. She instinctively recognises in McMurphy a threat, and therefore begins to try and erode his strength and independence by stripping away his identity. Note what McMurphy says to Harding about his understanding of what Nurse Ratched is trying to do:
It was the lady there that started it, made the mistake. I've known some peopl inclined to do that. I had this uncle whose name was Hallahan, and he went with a woman once who kept acting like she couldn't remember his name right and calling him Holligan just to get his goat.
The deliberate misnaming of McMurphy by Nurse Ratched is therefore the initial testing of her opponent in a conflict that comes to dominate the entire novel, as Nurse Ratched fights to maintain her control and order and McMurphy battles her to destroy that tight control she possesses.