Anyone who contends that Sofia Coppola's becoming a fashion designer is just one more example of a celebrity milking a name would hardly get an argument from her. In fact, she gives a wink and nudge to that contention in the collection's name, Milk.

But her mother, Eleanor, who attended her daughter's first runway show, at Bloomingdale's, said she had seen early signs of this career move."As a little kid, she was always drawing people in costumes, huge Victorian skirts or Little Bo-Peep," she said. When her husband, Francis Ford Coppola, was directing "Apocalypse Now" (and his wife kept the diary that became the documentary of the film, "Hearts of Darkness"), tiny Sofia would dance with the cinematographer, standing on his feet, then rush to a notepad and sketch the two of them dancing. Sofia's first costumes were the clothes for her father's segment of the film "New York Stories."

"She's fulfilling part of her natural childhood vision," Mrs. Coppola said. "She has a real fix on the time in which she lives, which is what an artist is, someone who resonates to the time she lives."

Part of having a fix on these times is understanding what to lash back against. So Sophia Coppola has a one shirt reading "Wasted" and the obligatory undermining-of-institutions shirt, hers in powder blue with "Tiffany & Co." printed on it (which Bloomingdale's is not carrying, for obvious reasons).

The most effective backlash is the one against technical training in fashion. "There are so many things I'm interested in that if I went to study them I'd never be able to do them," she reasoned.

Six camera crews came to film the modest show at Bloomingdale's.

"She comes prepackaged as the most well-known designer in juniors," said Kal Ruttenstein, the fashion director of the store. "It's the way she and all her friends in L.A. dress: little T-shirts and little skirts." The store sold 300 T-shirts in three days.

It may be a simple collection, but Coppola is not above getting the complex feelings designers experience before a show. "Is anyone here?" she asked before her L.A. friends-as-models took the runway. Ruttenstein replied, "The famous question of every fashion designer."