Split the_title

The best way to go about it is using the the_title filter. Put the following code in your functions.php.

add_filter( 'the_title', 'wpse_64467_prefix_title', '', 2 );
function wpse_64467_prefix_title( $title, $id ){
    $header_title = get_post_meta( $id, 'header_title', true );
    $title = ( $header_title ) ? $header_title . ' - ' . $title : $title;
    return $title;
}

Just replace header_title with the custom field name you are using.

UPDATE:
I guess google takes what it gets in the <title> tag in the head as the title. The above code won’t modify that. To modify the same you need to use the single_post_title filter in the following manner.

add_filter( 'single_post_title', 'wpse_64467_prefix_wp_title', '', 2 );
function wpse_64467_prefix_wp_title( $title, $post ){
    $header_title = get_post_meta( $post->ID, '_custom_text', true );

    $title = ( $header_title ) ? $header_title . html_entity_decode( ' – ', ENT_QUOTES, 'UTF-8' ) . $title : $title;
    return $title;
}

P.S – It would take time for the google results to reflect.