That a vendor might want to mark products they make is fine. It can be subtle and still work for legal purposes. It need not be ginormous and in your face. In the example of the floor mat in the OP the vendor's name could easily be on the bottom where it doesn't normally show.
An example of a project bicycle product that I no longer buy, for those unfamiliar with bicycle parts know that the smallest diameters are inside the frame and don't show:
This is their standard offering-
It used to be that you could special order them without the large "KING" engraving. The much smaller engraving is always there for reasons Chuck points out.
Can no longer make that special order. Now what they offer is this-
Which is obviously better, but not good enough for me. I now buy IRD headsets which do not have the engraving as standard, are sealed angular contact bearings, are available in the same range of colors, are nearly the same physical shape, and lack the Chris King surcharge. Ironically both come from Portland, OR.