This was the name of a 13th-century Italian saint who made clothes for the poor. As an English name, it has never been common.
Though long common as a Jewish name, Naomi was not typically used as an English Christian name until after the Protestant Reformation. A notable bearer is the British model Naomi Campbell (1970-).
In the United States this form was more popular than the full form Elizabeth from 1958 to 1978, and was in fact the top ranked American name between 1962 and 1969.