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I don't think it's very namey, what with the carn- reminding me of meat, and the -nation just being super noun-y. But as a middle name it'd be okay. It doesn't seem to refer to anything but the flower, so that's good.
I just now read that it is a word for complexion (skin tone?) in French.
I'd put it with a first name ending in A or maybe S.
I think if I wanted to refer to carnations I'd use Diantha (f) or Dianthus (m) instead. I'd probably also pronounce it dee- rather than die-.
Or there's Gilliflower, that'd be fun (maybe not referring to your exact favorite flower though).

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- mirfak