On first statement, the reference “design” is a noun and this property is associated with productName. The reference “productName” is an adjective. If you say “the design of ProductName”, you can also say “ProductName’s design”. Which one is perfectly correct depends on context and personal preferences, but one may sound or look that much better than the other in some circumstances.

To clarify, the rules governing case are identical to non-animal objects in the physical world.