<?php
$terms = get_the_terms( $post->ID, 'brand' );

if ( $terms && ! is_wp_error( $terms ) ) :

    $brand_links = array();

    foreach ( $terms as $term ) {
        $brand_links[] = $term->name;
    }

    $on_brand = join( ", ", $brand_links );
?>

<p class="brand">
    <span><?php echo $on_brand; ?></span>
</p>

<?php endif; ?>