I [name_f]LOVE[/name_f] the name [name_f]Poppy[/name_f] for a little girl, but only as a nickname. I think it would be strange once she is out of middle school. So, what names could go on the birth certificate?
What about [name_f]Pomona[/name_f]?
[name_f]Polly[/name_f]/[name_f]Pollyanna[/name_f]?
[name_f]Portia[/name_f]?
[name_f]Petra[/name_f]?
I think any P name practically could offer [name_f]Poppy[/name_f] as a nickname, including [name_f]Philomena[/name_f], a name I love.
[name_f]Penelope[/name_f] nn [name_f]Poppy[/name_f] has always been a huge favourite of mine 
Best of luck!
I love [name_f]Poppy[/name_f] as a standalone, but that aside:
[name_f]Penelope[/name_f]
[name_f]Philippa[/name_f]
[name_u]Piper[/name_u]
[name_f]Penelope[/name_f] my favorite full name for [name_f]Poppy[/name_f].
I also vote for [name_f]Penelope[/name_f]. I think it’s such a sophisticated yet spunky name with such versatility. [name_f]Poppy[/name_f] is a great nickname and like you said, if she gets older and wants a more “mature” nickname, she could always go for [name_u]Penny[/name_u], [name_f]Nell[/name_f], [name_f]Elle[/name_f], [name_f]Nellie[/name_f], [name_f]Ellie[/name_f], or even Lo.
[name_f]Penelope[/name_f]
[name_f]Philippa[/name_f]
[name_f]Parthenope[/name_f]
[name_f]Persephone[/name_f]
[name_f]Pomeline[/name_f]
[name_f]Calliope[/name_f]
[name_f]Ophelia[/name_f]
[name_f]Josephine[/name_f]
[name_f]Zipporah[/name_f]
[name_f]Penelope[/name_f]! I see that it has been suggested a few times already, but I think it’s the best full name for [name_f]Poppy[/name_f].
Edited for privacy.
I’m one of those that tends to think nicknames have to have full names that you can tell where the nickname came from 
[name_f]Penelope[/name_f] – I didn’t get this for a long time (sadly) but I finally do!
[name_f]Parthenope[/name_f]
Popea
Pompeya
Pompilia
Pomposa
[name_f]Amapola[/name_f] – it means “poppy”
[name_f]Rhea[/name_f] – one of it’s meaning is “poppy flower”