To hide an article title on an "Single article" menu item page, go to Menus and select the menu where the page lives (Main Menu, Footer Menu, etc).
Click the menu item linking to the article, then click the Options tab (see #1 below).
Change the setting for Title to Hide (see #2 below).
Then click Save & Close (see #3 below).
To hide a category title on a category blog menu item, go to Menus and select the menu where the menu item lives (Main Menu, Footer Menu, etc).
Click the menu item linking to the category, then click the Options tab.
Change the setting for Show Title to Hide (see below).
Then click Save & Close