No, the name can be used for a daylily or rose. It only means that Arctic Sun can't be used as the name for another Cornus cultivar. These trademarks don't apply to other genera.
The language against propagation means that the plant is patented, not copyrighted.
Your broad interpretation of the propagation ban probably is the correct one. At any rate, it's the one most people seem to accept. Even though there are no propagation police keeping you under surveillance, you should propagate patented plants only for your own use. You can't sell them or even give them to someone else for free.
