In Franz Kafka's The Metamorphosis, Gregor never wants to be called "the insect." One of the few things he finds pleasure in is feeling some small attachment to his family.
Gregor turns into "a gigantic insect" overnight. His family is repelled by him; arguably, the growing sense that he will no longer financially support them brings about their sense of separation from him—completing his sense of alienation and isolation. Because they seem to tolerate him because he support their comfortable lifestyle, it could be argued that his physical transformation simply mirrors his long-standing sense of emotional separation from them.
At first his sister shows concern and is supportive of him. When Gregor does not get on the train for work, chaos arises in the family's apartment; when his parents, and even someone from the company, are outside his room demanding that he appear, he notes:
Why didn't his sister join the others?
Symbolically, she is still on his side. For some time after Gregor's transformation, his sister Grete is the only connection he has with the outside world—it is she that comes in and feeds him.
Later, when Grete and their mother enter his room to remove furniture—another action that removes the human essence of his existence from his very surroundings—Gregor comes out of hiding and tries to protect a favorite picture on his wall. He defies his sister in this way; when their mother sees Gregor, she collapses. Clearly, Grete is furious with her brother, but still talks to him:
"Gregor!" cried his sister, shaking her fist and glaring at him. This was the first time she had directly addressed him since his metamorphosis.
Her anger foreshadows Grete's growing alienation from her brother.
Finally, when Grete plays the violin for the "lodgers", Gregor is greatly moved:
Gregor crawled a little farther forward...Was he an animal, that music had such an effect upon him?
This shows that he still does feel human inside.
However, it is at this point that Gregor's sister ultimately betrays her brother. And it is obvious not only by the decision she makes regarding Gregor's presence in the house, but in the way she refers to him:
"My dear parents...things can't go on like this. Perhaps you don't realize that, but I do. I won't utter my brother's name in the presence of this creature, and so all I say is: we must try to get rid of it. We've tried to look after it and to put up with it as far as is humanly possible, and I don't think anyone could reproach us in the slightest."
Not only does Grete now refuse to use her brother's name, but completely dehumanizes him by referring to him as "it," a thing—not a person.
Gregor, while unable to communicate with his family, has remained a part of their world by listening at the door. For instance, he has been eased by seeing his father take a job—he cleaning himself up each day and going out to earn a living. The family members find a way to sustain themselves financially after Gregor can no longer work. His observations and concerns for his family show that Gregor is still human within. While his appearance may have changed dramatically, he remains the loving son and brother that he always was. It is his family that changes. It can be argued that once they agree to get rid of him, his last link to his family—and his old life—is severed, and he dies.
Gregor always prefers his name to "it," and has still felt human till the story's end.