How to remove “Taxonomy name:” from wp_title

Use wp_title filter to control output

function mamaduka_remove_tax_name( $title, $sep, $seplocation ) {
    if ( is_tax() ) {
        $term_title = single_term_title( '', false );

        // Determines position of separator
        if ( 'right' == $seplocation ) {
            $title = $term_title . " $sep ";
        } else {
            $title = " $sep " . $term_title;
        }
    }

    return $title;
}
add_filter( 'wp_title', 'mamaduka_remove_tax_name', 10, 3 );