Hi,
This setting is to display or not the label before the dropdown on the product page.
So what you could do is to turn off that setting, in order to not have the labels displayed on the product page, and then change the values so that instead of "A", "B", etc you would have "Cup A", "Cup B", etc
That way, you would get the "Cup" in the email and other places like you want.
Otherwise, to keep the values as you have them now, and add the characteristic name, it would require modifying the code
$variant->characteristics_text .= $separator . $char_value;
in the file administrator/components/com_hikashop/classes/product.php
I don't recommend this as it's not easy, and it means you'll loose the changes when you update HikaShop, having to apply the change after each update.