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).
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.
A famous bearer of this name is a little bratty girl in the show Naruto, who, along with her friends, helped tease a young Sakura Haruno because of her forehead (kids called her "billboard-brow" because she has such a huge forehead). Kasumi and her friends were chased away by an angry Ino Yamanaka (Sakura's best friend).
I like this name. To me, it doesn't have that bad of the association with the nasty Pokémon character that Misty has, despite it being her Japanese name.
Also the name of the "busty" heroine of the Dead or Alive video game series. Kasumi's an orange-haired female ninja and a bit of a pervy geek's fantasy; but she has a noble, sweet and courageous nature.