The name of women's organisation that called for "full participation of women in mainstream American society" is The National organisation for Women(NOW).
Explanation:
Betty Friedan published a book struck a nerve, within the three years of publication of her book a new feminist movement took birth which had been absent since suffrage movement. In 1966, Friedan, and others formed an activist group called the National Organization for Women.
NOW was dedicated to the "full participation of women in mainstream American society." They demanded equal pay for equal work and pressured the government to support and enforce legislation that prohibited gender discrimination.