single zen cart for different shops. I would like to know how can we add a shop name along with each product in zen cart (in the sql table)
You haven't said whether the shops share the same products, but usually in this setup they do. If so, then adding the store name to the database would not be what you want to do, as the store name you add there would also be displayed on the other shops.
Instead you would have to either ...
catch the data as it is pulled from the data base (this normally happens in the includes/modules/pages/PAGE_NAME/header_php.php file for the center box content or the includes/modules/sideboxes file for sideboxes such as new products, specials
... or ...
catch the data at the point of display in the relevant page template or sidebox template files.