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I checked your interpretation of Kazumi = kazu (harmony, peace) + mi (beauty). And indeed, the most frequent kanji writing of the name that I could find was this combination:
和美

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This should answer the original poster's question about Kazumi.

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But what now about Kasumi = mist, according to BtN? It seems that Kazumi and Kasumi are two different names, and the most frequent kanji writing for Kasumi seems to be the kanji for "mist":
霞

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And finally, just to make it a little more complicated still, there is a third, very similar, but distinct given name Katsumi, this time mostly male instead of female like Kazumi and Kasumi. It seems to be frequent among Japanese men that are already somewhat older, and is frequently written with the two kanji meaning "self-control":
克己

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But anyway, I found much confusion about this tripple of names:
- All three have alternative kanji writings and thus other meanings as well
- I am not sure, but I think for all three names I saw examples of the oposite sex carrying the name, i.e. male Kasumi's and Kazumi's
- The Romanization is not consistent, with people sometimes writing Katsumi when they should write Kazumi, and writing Kazumi when they should write Kasumi, and so on...

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Rene     www.AboutNames.ch