functions.php

/**
 * Print the product's vendor name before the product title in the loop.
 *
 * @return void
 */
function wc_vendors_name_loop() {
    $vendors = get_the_terms( get_the_ID(), 'shop_vendor' );

    if ( $vendors && ! is_wp_error( $vendors ) ) {
        foreach ( $vendors as $vendor ) {
            $all_vendors[] = '<a href="' . get_term_link( $vendor, 'shop_vendor' ) . '" title="' . $vendor->name . '">' . $vendor->name . '</a>';
        }

        $vendors = join( ", ", $all_vendors );

        echo '<span class="shop_vendors">' . $vendors . '</span>';
    }
}
add_action( 'woocommerce_before_shop_loop_item_title', 'wc_vendors_name_loop', 20 );