Slightly Dangerous (1943) on Netflix

Peggy is 21 and bored. She has just been awarded a certificate for starting work on time for 1000 days. She decides that she needs a change so she leaves a note, which is taken to be suicidal, and heads for New York where she gets a make over. A new outfit, a new look and an freak accident gets her in the paper as a amnesia victim, just because she does not want to be Peggy Evans any more. The paper thinks she may be an heiress so she searches for a few clues from back issues of the paper and finds that Carol Burden was never found. Cornelius Burden, however, has sent dozens of frauds to jail already and she must trick him and Baba to keep out of jail. Next, she must stop her old manager, Bob Stuart, from spilling the beans about her.