While it might be authentic, Walker suggest that Dee wants to change her cultural identity because it is "fashionable."
It is evident that Mrs. Johnson loves both of her daughters. However, she is keenly aware of Dee's penchant for social acceptance. Her narration features comments that reflect how Dee is mindful of appearances and crafts herself accordingly. Statements such as "Dee wanted nice things" display this. Mrs. Johnson'a insight extends to how she did offer the quilts that Dee now covets. However, Dee rejected the gesture saying that, they were "old fashioned" and "out of style."
The desire for social acknowledgement motivates Dee to want to change her identity. She realizes that embracing a more nationalistic image is "in" and will appeal to people. Presumably, this is the reason that Dee is with Hakim- a- Barber. Mrs. Johnson notes that Dee has always "held life in the palm of one hand." This shows how Dee is aware of what people want. Right now, it is the embrace of heritage. That is why she says that her old name is "dead" and that she "couldn't bear it any longer, being named after the people who oppress me." Dee knows how this will play out to Hakim- a- Barber. A statement like that enhances her image.
When Dee is in the car and bids her mother and sister farewell, she impresses on Maggie how she "ought to try to make something of yourself" and that "it's a new day." Dee might believe these words. However, she waits to say them when she is in the car with Hakim- a- Barber. This displays another way how Dee's desire the change her cultural identity is image based.