Joy's mother suspects that the name Hulga is selected because it is the ugliest name that Joy could find. According to Joy/Hulga this is exactly the case.
Joy/Hulga is a somewhat bitter young woman and one of her passions is to clearly demonstrate that her mother's views on the world are innaccurate. She resents the views which her mother simplistically espouses as well as the expectations her mother holds for her, saying at one point, " “If you want me, here I am—LIKE I AM.” Joy/Hulga refuses to become what her mother wants her to be.
In keeping with this aim, she changes her name. This does two things for Hulga. It erases her mother's creative act of naming her in the first place and it shows that her mother gave her the wrong name.
“One of her major triumphs,” the narrator says, “was that her mother had not been able to turn her dust into Joy, but the greater one was that she had been able to turn it herself into Hulga.
Joy/Hulga is not joyous. She feels that she is ugly and has no place in her community.
Hulga’s wooden leg makes her grotesque...
She is not like other people and she does not want to be. She does not even want to be accepted. There is part of Hulga also that wants others to join in with her view of reality. She tells Manley at one point that “we are all damned.”
All of these tendencies and beliefs, on her part, are clearly communicated in the name she has chosen. The name, then, becomes a corrective act regarding her mother's erroneous views on the world and becomes a communicative act as well.