Where I live, supermarkets must write in the package who is making their off-brand products so you can know who are you giving your money to.
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They're not really no-name brands. They're all house brands, but Lidl decided that putting their name and design on most of the products in the store was a little too in your face. To give the illusion of choice to the customer, they created a bunch of brands, each with their own design.
They also should kinda resemble the original product
Not just in taste (or smell, when it comes to perfumes, as I've recently heard they have as well), but also in packaging and naming
That way customer also know much better what to expect with the copy cat product