I think Penelope is the most obvious.
I'm going to go on a limb and say that Poppy is such a sweet and affectionate sounding name that while it would be nice if it were to actually have a concrete connection to the formal name, I don't really think it has to. If you're not into any of the suggested fuller names and you are set on Poppy, take that into consideration.
On a side note - I think there has been a thread on Poppy before, and responses were that it brought to mind either a) a grandfather, or b) an affectionate Spanish term connoting a boyfriend of some sort. Just throwing that out there.