Okay, I'm thinking about how this can be fixed, but I don't know how complicated the programming would be.
Can the roses be listed under each of their names (which would preserve the alphabetical order) and have all of the information automatically be copied to each name?
That's how helpmefind.com is set up. The same information and photos are accessible under any of the alternative names.
In that case, there would be no need to have one of the names be the main one.