I think the easiest solution is just to pick a name with these names as easy nicknames. I really don’t know any dogs by those names (but I know dogs by lots of people names, it’s just something people do nowadays), so she shouldn’t worry so much probably, but at the same time, I’m a fan of not using nicknames as full names.
Are all nice names that are varying degrees of mainstream and out there but nothing too out there.
[name]Poppy[/name] could be [name]Penelope[/name] or maybe [name]Philippa[/name] or even just a nickname for an unrelated name.
[name]Posey[/name] is used as a nickname for [name]Josephine[/name].
Hopefully that gets her started.
She could also do a [name]Rose[/name] middle name or [name]Poppy[/name] as a middle name and call the girl that.
Good luck to her!