Change recent posts widget title

I had a similar situation. Add the following code to your functions.php and see if it works for you.

function my_widget_title($title, $instance, $id_base) {
     if ( 'recent-posts' == $id_base) {
        return __('New Title');
      }  
      else {
        return $title;
      }  
}

add_filter ( 'widget_title' , 'my_widget_title', 10, 3); 

Note: this will change the title of all the “Recent Post” widgets.