You're missing my point. I'm saying that plants with vastly differing characteristics can be classified as the same species, so the fact that one Achillea has different leaves and a different height does not necessarily put it in a different category than others. It's true that Brussels Sprouts and Turnips have different common names, which I assume is the "third name" you mention, but they are not differentiated by their species name. You can always include your preferred name (the synonym) in your photo caption if you wish.
