Вы должны написать так
В модели продукта
public function category()
{
return $this->belongTo(Category::class);
}
В Ctonroller
$products = Product::with('category')->paginate()
В Blade
@foreach($products as $product)
<tr class="product">
<td>{{ $product->product_name }}</td>
<td>${{ $product->price }}</td>
<td>{{ $product->category->name }}</td>
<td>{{ $product->product_description }}</td>
<td><a href = 'delete/{{ $product->product_id }}'><button type="button" class="btn btn-danger">Delete</button></a></td>
@endforeach