Should I use a separate table to store image file names?
I think it's better to let the images have their own table. The way I've solved it is by having 3 tables.

One for the products, another one for the images
and the third for the connections.


The product table just stores information about the product and nothing about the images.
The image table just stores the image id and file extension (the image id is also the filename).
The "connections"-table stores image id and product id so that you know which image belongs to which product.




Though, if only one image can be connected to one product you only need two tables. The product table and image table. The product table is just like above but the image table now contains a third column, productid. Now you can easily see which image belongs to which product.