Kasumi

Kasumi and Kazumi are separate names and pronounced differently with a definite distinction between the s and the z. You don't drop the u in these 2 names (though you can drop the u in the pronunciation of Kazuko so it sounds like Kazko).

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Multiple kanji possibilities for this name result in multiple meaning possibilities and you can use 2 kanji or 3, depending on what you choose for the name, as long as you get the syllables in.

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"ka"
-fragrance
-beautiful
-song

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"su"
-sun/day
-joyous (celebration)

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"mi"
-beautiful
-fruit

I have also heard of Kasumi being spelled Kazumi. Personally, I like "Kazumi" better than "Kasumi", although they both mean "mist".