I was surprised to learn that 直美 isn't spelled out using katakana and, according to Wikipedia:
Naomi (なおみ, ナオミ), pronounced [naomi] is a Japanese name. Though it is a unisex name, it is primarily used by women. Naomi can be spelled using hiragana, katakana, kanji, or a combination of kana and kanji. For example;
...my question is, did the Japanese name predate (or develop separately from) the Western name? Is this just a coincidence?