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.
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-).
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.