Go to options and r1 all the way to the last screen I. Menus top option should say log off under should say switch character

Which sign out button are you looking for? On Destiny? The sign out in Destiny is in the menu. Hit the menu button for your respective system and hit the shoulder button to the right until you get to the settings/logout area. For Xbox you can select change character and then close the game. For PS4 you can actually select log out. Hope that helps!