In August, Ms. Zuckerberg, 29, quit her job at Facebook, where she had been among the first two dozen people hired. Most recently, she was the director of marketing. In its early days, Ms. Zuckerberg was a buoyant presence, representing her reticent brother to an eager press. Later, she earned attention (not always favorable) singing at company functions with a band composed of colleagues. And she came up with the idea for Facebook Live, the social network’s video channel, which has featured interviews conducted by Facebook executives with Oprah Winfrey and President Obama. Now Ms. Zuckerberg has started her own business, R to Z Media, to help companies take advantage of social media.