Unlike the other IJN Destroyers, Kamikaze and her sisters wear traditional japanese clothes, namely a pink hakama over a red kimono paired with lace-up boots in the style of a Meiji schoolgirl uniform, which references how she and her sisters were made during the Taisho era (when this style of dress was still prominent).
She doesn't want to be seen as being old, despite being of the oldest destroyer class in the game and her old-fashioned looks. That being said, she has an excellent war record for her capabilities.
Her first Seasonal CG for Valentines 2018 consists of her wearing an apron, a maid headdress and a hair flower while her sleeves are not held with a tasuki and the ends of her hair ribbon have been made exposed. She is carrying a large present shaped like a torpedo casing, either a large chocolate or a box filled with many smaller chocolates, but fan speculation is rampant.
Kamikaze is also related in some way to all four of the Myoukou-class:
Despite similarity in names, Kamikaze and the Kamikaze-class do not have any relation to the so-called "kamikaze pilots," officially the Tokubetsu Kougekitai (特別攻撃隊, "special attack unit") or Shinpuu Tokkoutai (神風特攻隊), that conducted suicide attacks on Allied ships later in World War II (as pointed out by post #2351490).