Lynn, you're thinking on the right track, but synonyms are for botanical name synonyms (genus and species only).
The more I think about this, I am thinking that the best solution is going to be to add an extra field for "Other cultivar names". Then you would enter any additional cultivars into that field, and program it to work just like the extra common names and extra synonyms, where you can add multiple cultivar names, each in their own field, through the "Edit plant name" area.
