You'll need to edit your includes/modules/product_listing.php (OR if you have an override, includes/modules/YOUR_TEMPLATE/product_listing.php).
Find:
case 'PRODUCT_LIST_NAME':
$lc_align = '';
$lc_text = '<h3 class="itemTitle"><a href="' . zen_href_link(zen_get_info_page($listing->fields['products_id']), 'cPath=' . (($_GET['manufacturers_id'] > 0 and $_GET['filter_id'] > 0) ? zen_get_generated_category_path_rev($_GET['filter_id']) : ($_GET['cPath'] > 0 ? zen_get_generated_category_path_rev($_GET['cPath']) : zen_get_generated_category_path_rev($listing->fields['master_categories_id']))) . '&products_id=' . $listing->fields['products_id']) . '">' . $listing->fields['products_name'] . '</a></h3><div class="listingDescription">' . zen_trunc_string(zen_clean_html(stripslashes(zen_get_products_description($listing->fields['products_id'], $_SESSION['languages_id']))), PRODUCT_LIST_DESCRIPTION) . '</div>';
break;
and replace with:
case 'PRODUCT_LIST_NAME':
$lc_align = '';
$lc_text = '<h3 class="itemTitle"><a href="' . zen_href_link(zen_get_info_page($listing->fields['products_id']), 'cPath=' . (($_GET['manufacturers_id'] > 0 and $_GET['filter_id'] > 0) ? zen_get_generated_category_path_rev($_GET['filter_id']) : ($_GET['cPath'] > 0 ? zen_get_generated_category_path_rev($_GET['cPath']) : zen_get_generated_category_path_rev($listing->fields['master_categories_id']))) . '&products_id=' . $listing->fields['products_id']) . '">' . $listing->fields['products_name'] . '</a></h3><div class="listingDescription">' . zen_get_products_description($listing->fields['products_id'], $_SESSION['languages_id']) . '</div>';
break;
This will keep the title using product name. If you want to omit the product's name any ONLY show the description (as in your mockup), you'll be editing the same lines, but will replace it with this:
case 'PRODUCT_LIST_NAME':
$lc_align = '';
$lc_text = '<div class="listingDescription">' . zen_get_products_description($listing->fields['products_id'], $_SESSION['languages_id']) . '</div>';
break;