I like both names and think they go fine together. Plus, even if they didn't (which I don't think is the case), you hardly ever say someone's full name anyway so not really an issue IMO.
I think 'Poppy' will be fine on a 'grown woman' since a lot of names like Poppy are quite popular at the moment so when she is grown up it will be quite normal!
It's a bit like how it's hard to imagine certain 'old lady' names on a baby at the moment - when those old ladies were babies it obviously sounded perfectly reasonable!