Marissa Mayer, one of the top executives at Google, will be the next C.E.O. of Yahoo, making her one of the most prominent women in Silicon Valley and corporate America. The appointment of Ms. Mayer, who was employee No. 20 at Google and was one of the few public faces of the company, is considered a surprising coup for Yahoo, which has struggled in recent years to attract top flight talent in its battle with competitors like Google and Facebook.