[name]How[/name] about [name]Nixie[/name]? Or [name]Ruby[/name]? Or [name]Xanthe[/name]? Or [name]Io[/name]?
I love [name]Amelia[/name]- nn [name]Mia[/name]. I think [name]Poppy[/name] and [name]Amelia[/name] sound lovely together 
[name]Gracie[/name]
I love the suggestion of [name]Fifer[/name]…I think that’s adorable.
I don’t think anyone has mentioned [name]Hazel[/name] yet.
Thanks everyone for your input and help! We have decided… she will be [name]Clare[/name] [name]Alice[/name]
[name]Clare[/name] [name]Alice[/name] is a lovely name, and goes well with [name]Poppy[/name] [name]Anne[/name]!
[name]Clare[/name] [name]Alice[/name] is lovely! 
GAH! Back to the drawing board. I don’t like [name]Clare[/name] anymore. It does sound too dull next to [name]Poppy[/name]. HELP!
[name]Edie[/name] - but there’s the ice cream. And the nick-namey feel to it
[name]Clementine[/name] - but what to call her for short?
I need ideas - AGAIN!
I don’t why ,but, evertime I hear [name]Poppy[/name] I think [name]Willow[/name]. Also I think [name]Faye[/name], [name]Rue[/name], [name]Maisy[/name], [name]Iris[/name], and [name]Noelle[/name].
Also, some nn’s for [name]Clementine[/name] could be [name]Clemmie[/name], [name]Tina[/name], [name]Emmie[/name], [name]Emmy[/name], [name]Lemmie[/name], [name]Cleo[/name], [name]Clem[/name], [name]Tiny[/name].
I think [name]Poppy[/name] and [name]Clementine[/name] is cute! For nn’s, how about [name]Cleo[/name], [name]Emme[/name], or [name]Minnie[/name]?
[name]Clementine[/name] sounds lovely next to [name]Poppy[/name]!
NN include:
[name]Clem[/name]
[name]Emme[/name]
[name]Emma[/name]
Lemen
Ennie
[name]Enna[/name]
[name]Minnie[/name]
[name]Mimi[/name]
[name]Mia[/name]
[name]Lem[/name]
I love [name]Edie[/name]! it also sounds lovely with [name]Poppy[/name], I personnally like [name]Edith[/name] nn [name]Edie[/name], it too sounds great with [name]Poppy[/name].
Some others that sound great with [name]Poppy[/name]:
[name]Mollie[/name] ([name]Mollie[/name] [name]Malone[/name])
[name]Lucy[/name] ([name]Lulu[/name], [name]Lou[/name])
[name]Ruby[/name] ([name]Rue[/name], Rubes)
[name]Lilou[/name] ([name]Lila[/name], [name]Lily[/name], [name]Lulu[/name])
[name]Jade[/name] ([name]Jay[/name], [name]Ada[/name])
[name]Lilo[/name] ([name]Lee[/name])
[name]Stella[/name] (Stelles, Stellie, [name]Ella[/name])
[name]Tessa[/name] ([name]Tess[/name])
[name]Eleni[/name] ([name]Lanie[/name], [name]Ellie[/name], [name]Annie[/name])
[name]Elin[/name] ([name]Nell[/name])
[name]Lila[/name] ([name]Lily[/name])
[name]Lilac[/name] ([name]Lila[/name], [name]Lily[/name])
[name]Quinn[/name]
[name]Becca[/name] ([name]Beck[/name])
[name]Olive[/name] ([name]Ollie[/name], [name]Liv[/name])
[name]Clio[/name] (Clee, [name]Lio[/name], [name]Ollie[/name])
[name]Calla[/name] ([name]Kay[/name], Ayllie, [name]Callie[/name], [name]Allie[/name])
[name]Lotus[/name] ([name]Lottie[/name], [name]Lola[/name])
I hope this helps:)
[name]Isabel[/name]
[name]Edie[/name] - I can’t comment on the ice cream, as I don’t think we have it here in [name]Britain[/name] (I’m doing a mental scan and can’t remember seeing any ice cream branded [name]Edie[/name]). But, while I normally advocate using the full name, I don’t think the nickname-y feel of [name]Edie[/name] would be such a problem, as [name]Poppy[/name] has that feel, too, due to the -ee ending sound and relatively short nature of it. Alternatively, you could use the initials [name]ED[/name] and use the nn [name]Edie[/name].
[name]How[/name] about (I think these all sit well next to [name]Poppy[/name] [name]Anne[/name]) :
[name]Elizabeth[/name]
[name]Eliza[/name]
[name]Elsa[/name]
[name]Esther[/name]
[name]Eulalie[/name]
[name]Evadne[/name] (e-VAD-nee)
[name]Evangeline[/name]/a
[name]Eloise[/name]
[name]Elodie[/name]
Elowen
[name]Eleanor[/name]
[name]Electra[/name]
[name]Eleri[/name]
[name]Elva[/name]
[name]Evelyn[/name]
[name]Elvira[/name]
[name]Esme[/name]
[name]Estelle[/name]/a
[name]Daphne[/name]
[name]Dahlia[/name]
[name]Delia[/name]
[name]Delphine[/name]/a
[name]Dorothy[/name]
[name]Dorothea[/name].
[name]Clementine[/name] is very pretty, and makes a sweet sister to [name]Poppy[/name] despite the difference in length of the names. Nicknames [name]Clem[/name], [name]Clemmie[/name] or [name]Emmie[/name] are the most appealing, in my opinion. You might like [name]Camelia[/name], too, although it would start a flower theme.
Good luck! [name]Auburn[/name]
[name]Clementine[/name] is lovely with [name]Poppy[/name]! To me, both names are very spunky and colorful, so I think that they match well. The previous posters have already mentioned most, if not all, the nicknames for [name]Clementine[/name] - my personal favorite is [name]Cleo[/name], which also sounds good next to [name]Poppy[/name], I think. [name]Edie[/name] is cute, too, but I agree that it feels too nicknamey - I prefer [name]Edith[/name] “[name]Edie[/name]”, but that feels a bit mismatched with [name]Poppy[/name] (to me, [name]Edith[/name] is “old lady” - that’s not a bad thing, and I do like the name - whereas [name]Poppy[/name] feels more youthful). Also, [name]Edie[/name] has two syllables and the “-ee” ending, so [name]Poppy[/name] and [name]Edie[/name] might be a bit matchy…
On Nameberry’s page on [name]Poppy[/name], there’s a box that says “People who like [name]Poppy[/name] also like: [name]Adelaide[/name], [name]Adeline[/name], [name]Nora[/name], [name]Stella[/name], [name]Beatrix[/name], [name]Daisy[/name], [name]Delilah[/name], [name]Eliza[/name], [name]Lily[/name], [name]Lulu[/name], [name]Lydia[/name], [name]Piper[/name], [name]Violet[/name]…” I think that some of them - [name]Daisy[/name], [name]Lily[/name], [name]Piper[/name], [name]Violet[/name] - are a bit matchy, which may or may not bother you, but there are some that I can easily picture with [name]Poppy[/name]… From [name]Clementine[/name]'s page, there’s [name]Ada[/name], [name]Elizabeth[/name], [name]Cora[/name], [name]Eden[/name], [name]Olivia[/name], [name]Sophia[/name], [name]Tallulah[/name], and [name]Willow[/name]. [name]Maeve[/name] and [name]Maisie[/name] are listed for [name]Edie[/name].
A few more:
[name]Eloise[/name]
[name]Fiona[/name]
[name]Gemma[/name]
[name]Isla[/name]
[name]Susannah[/name]
[name]Willa[/name]
[name]Zara[/name]
Good luck!
I second [name]Poppy[/name] and [name]Nora[/name] or [name]Poppy[/name] and [name]Gemma[/name]! Too cute!