A third proposal by the company, Psy-Group, which is staffed by former Israeli intelligence operatives, sketched out a monthslong plan to help Mr. Trump by using social media to help expose or amplify division among rival campaigns and factions. The proposals, part of what Psy-Group called “Project Rome,” used code names to identify the players — Mr. Trump was “Lion” and Mrs. Clinton was “Forest.” Mr. Cruz, who Trump campaign officials feared might lead a revolt over the Republican presidential nomination, was “Bear.”