I'm not sure I know the answers to all of these questions, but I think a trademarked name only protects the name. The trade mark or copyright precludes someone else's use of the same name for a different cultivar. Patenting is what protects the hybridizer against propagation by another commercial entity. Patented plants don't necessarily have a trademarked name.
Keeping track is sometimes a simple matter and sometimes more complex. In the rose market, grafted patented roses are sold with a metal tag, issued by the patent holder to the grower. The grower pays royalties to the patent holder for each metal tag issued and is forbidden to sell anything without a metal tag. Own-root patented roses are a different matter and less simple to control. There are no metal tags involved, and the grower pays royalties on the honor system, leaving considerable room for patent abuse.