You could randomize the array with array_rand which will return the key, and then use array_flip to switch the key with the value (ie get your random title).
Hook into save_post, so the random title is assigned and update the DB when you actually publish a post as opposed to using the_title filter.
function save_title( $post_id ){
global $wpdb;
$title = array (
'1' => 'another title',
'2' => 'here is again, a title',
'3' => 'random titles',
'4' => 'RANDOM TITLE',
'5' => 'ANOTHER RanDom TiTlE!',
'6' => 'titles everywhere'
);
$wpdb->update( $wpdb->posts,
array( 'post_title' => array_rand( array_flip( $title ) ) ),
array( 'ID' => $post_id ) );
}
add_action( 'save_post', 'save_title');