functions.php

add_action( 'woocommerce_archive_description', 'show_vendor_name_archive', 5 );
function show_vendor_name_archive() {
    global $wp_query;

    $term =	$wp_query->queried_object;

    if ( ! is_object( $term ) || empty( $term->term_id ) ) {
        return;
    }

    if ( is_tax( WC_PRODUCT_VENDORS_TAXONOMY, $term->term_id ) ) {
        echo '<h3>' . $term->name . '</h3>';
    }
}