I think the Hunger Games has made the name more unusable. Now it will be what most people associate it, and though you say that you are okay with this association I think currently it is a very big one. Like calling your daughter
Hermione.
Other than that; I've got to say it is not one of my favoured flower names. As overused as it is, I prefer
Rose on it's own or as a nickname for something like Roseanna,
Rosalie etc. I dislike "Prim" - as it reminds me of the phrase "prim and proper" meaning quite stuck up and untarnished. For me it would work better in the middle name spot becuase of the Hunger Games and "prim" associations.