How To Change Logout Screen Title

First of all, if you see this page it means you’re doing logout in a wrong way. The check_admin_referer() fails and calls wp_nonce_ays(), thus prompting for a confirmation (ays = Are You Sure?). See these threads for more details:

• How to log out without confirmation ‘Do you really want to log out?”?
• WordPress failure when logging out
• wp_logout_url() – WordPress Failure Notice

Finding and eliminating the cause of the problem may be the best way to go.

The text string itself is on line 2607 of wp-includes/functions.php:

wp_die( $html, __( 'WordPress Failure Notice' ), 403 );

As you see, there’s no filter. However, it’s a string passed to __() function, which means you can filter it using gettext:

function wpse283987_change_string( $translated_text, $untranslated_text ) {

    global $pagenow;

    if( $pagenow === 'wp-login.php' && $untranslated_text === 'WordPress Failure Notice' ) {
        return __( 'Your New Text' );
    }

    return $translated_text;
}
add_filter( 'gettext', 'wpse283987_change_string', 20, 2 );