Locally, they are known as the former and I do get some looks and corrections periodically. I sometimes like to get digs in to people by repeating the correct pronunciation. The peony pictured here is a nice yellow we purchased recently. Yellows are a difficult color to acheive in peonies. We actually were eyeing another one but decided not to shell out the dough for it and go for this one which should have been orange and yellow. Hmmm, appears that luck was on our side!
Of course Peonies are not the only flower that has its local name. My personal favorite is the Clematis. Until I moved here, to Paris Tn., I don't know that I had ever heard it pronounced any way other than CLEM-it-tus.
Or maybe time and fading memory are just failing me now, who knows. But here, they are known as Cle-MAT-us. This is the one I pariticularly love to torment people with by never conforming to the local pronunciation. Sometimes people even have to ask me if we are talking about the same plant. (I get a big inward grin when that happens, hehehe) I love clematis. I love anything that vines and twines, but when it flowers like a clematis, its a real winner! This one is growing in our garden; scaling an old spoked wagon wheel I found just for this reason. 
With so many plants having dual pronunciations, I could go on and on, but will close with the title theme, the Lycoris. LY-cor-us or ly-COR-us? Resurrection lillies or Spider lilies? I prefer just calling them naked ladies. Now, come on, who's gonna complain about having naked ladies in their garden no matter how you say it??
