Hi,
The setting Jerome talks about is what you're looking for.
The display of the name of the vendor on the product page is not linked to that setting.
You need to create a HikaShop content module instance via the Joomla modules manager and first configure it to display all the products of the shop by selecting the main category (it should be the case by default), and setting the "sub element filter" setting to "all sub elements" in that module. Then, when you turn on the "filter same vendor" setting, it will remove all the products that aren't from the same vendor of the current product on the product page.
If that's not the case, then you have a problem in the settings of your module. In that case, please provide screenshots of its settings and a link to a product page linked to a vendor with other products so that we can analyse the situation.