How to format text of site subtitle

If you output the description with bloginfo(), you can use the filter bloginfo.

add_filter( 'bloginfo', 'wpse183972_description_italic', 10, 2 );
function wpse183972_description_italic( $text, $show )
{
    if ('description' == $show) {
        $word = 'WordPress';
        $text = preg_replace( '^(' . preg_quote( $word ) . ')^', '<em>$1</em>', $text );
    }
    return $text;
}