Hi Dario,
manufacturers are saved in the #__j2store_manufacturers table but the full information can be found in the #__j2store_addresses table. So the brand name is the 'company' column of the latest.
When on a products list page, when iterating through the list (the product itself could be $item or $product depending on how the page is built), the brand name would be $item->brand_name or $product->brand_name, like I sugested in my previous answer.
The overrides go to your default template, under the html/com_j2store/templates/bootstrap5 folder.
You need to copy the files from plugins/j2store/app_bootstrap5/app_bootstrap5/tmpl/bootstrap5 and paste them in the overrides folder. I think the ones starting with default should be enough.
In default.php, you can see:
<?php foreach($this->products as $product):?>
This is where the loop is.
Now, if you want to add the brand name in a specific area for a product, you prodably have to override, for the simple product, for instance: default_simple.php.
In that file, you will want to add something like:
<?php if (!empty($this->product->brand_name)) : ?>
<div class="manufacturer"><?php echo $this->product->brand_name; ?></div>
<?php endif;?>
That should do the trick!