Mulholland Drive

The story may not be linear and exhibits several instances of temporal disruption. A dark-haired woman (Harring) escapes her own murder, surviving a car accident on Mulholland Drive. Injured and in shock, she descends into Los Angeles and sneaks into an apartment that an older, red-headed woman has just vacated. An aspiring actress named Betty Elms (Watts) arrives at the same apartment and finds the dark-haired woman confused, not knowing her own name. The dark-haired woman assumes the name "Rita" after seeing a poster for the film Gilda (1946), starring Rita Hayworth. To help Rita remember her identity, Betty looks in Rita's purse, where she finds a large amount of money and an unusual blue key.
In what seems to be a scene from a different narrative, set at a diner called Winkies, a man (Patrick Fischler) tells his companion (Michael Cooke) about a nightmare in which he dreamt there was a horrible figure behind the diner. When they investigate, the figure appears, causing the man with the nightmare to collapse in fright. As the principal narrative resumes, Hollywood director Adam Kesher (Justin Theroux) has his film commandeered by apparent mobsters, who insist he cast an unknown actress named Camilla Rhodes (Melissa George) as the lead in his film. After he resists, he returns home to find his wife having an affair and is thrown out of his house. He later learns that his bank has closed his line of credit and he is broke. He agrees to meet a mysterious figure called The Cowboy, who urges him to cast Camilla Rhodes for his own good. Later, a bungling hit man (Mark Pellegrino) attempts to steal a book full of phone numbers and leaves three people dead.
Trying to learn more about Rita's accident, Betty and Rita go to Winkies and are served by a waitress named Diane, which causes Rita to remember the name "Diane Selwyn". They find Diane Selwyn in the phone book and call her, but she does not answer. Betty goes to an audition, where her performance is highly praised. A casting agent takes her to the set of a film called The Sylvia North Story, directed by Adam, where Camilla Rhodes gives an audition and Adam declares, "This is the girl." Betty smiles shyly as she locks eyes with Adam, but she flees before she can meet him, saying that she is late to meet a friend.
Betty and Rita go to Diane Selwyn's apartment and break in when no one answers the door. In the bedroom they find the body of a woman who has been dead for several days. Terrified, they return to their apartment, where Rita disguises herself with a blonde wig. The two women have sex that night and awake at 2 a.m., when Rita insists they go to an eerie theater called Club Silencio. On stage, a man explains in several languages that everything is an illusion; a woman begins singing then collapses, although her vocals continue. Betty finds a blue box in her purse that matches Rita's key. Upon returning to the apartment, Rita retrieves the key and finds that Betty has disappeared. Rita unlocks the box, and it falls to the floor with a thump.
The older red-headed woman investigates the sound, but nothing is there. The Cowboy appears in the doorway of Diane Selwyn's bedroom saying, "Hey, pretty girl. Time to wake up." At this point, all elements of the narrative seem to change. Diane Selwyn (played by Watts) wakes up in her bed. She looks exactly like Betty, but is portrayed as a failed actress driven into a deep depression by her unrequited love for Camilla Rhodes (played now by Harring). On Camilla's invitation, Diane attends a party at Adam's house on Mulholland Drive. Her limousine stops before they reach the house and Camilla escorts her using a shortcut. Adam appears to be in love with Camilla. Over dinner, Diane states that she came to Hollywood when her aunt died, and she met Camilla at an audition for The Sylvia North Story. Another woman (played by George) kisses Camilla and they turn and smile at Diane. Adam and Camilla prepare to make an important announcement, and dissolve into laughter and kiss while Diane watches, crying.
Diane meets with the hit man at Winkies, where she gives him Camilla's photo and a large amount of money, and they are served by a waitress named Betty. The hit man tells Diane that when the job is done, she will find a blue key. Diane asks what, if anything, the key opens, but the hit man just laughs. Diane looks up and sees the man who had the nightmare standing at the counter. Back at her apartment, with the key on a table in front of her, she is terrorized by hallucinations. She runs screaming to her bed, where she shoots herself. A woman at the club whispers "Silencio".

Question: How does the dark haired woman choose the name Rita?
Answer: She sees a poster for the film Gilda, starring Rita Hayworth.