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Maybe it is something along those lines. Like you said the girl in the novel is Japanese, so it wouldn't work if she carried a completely foreign name, but a name that could possibly exist in Japanese as well, and yet wasn't used at that time. So this is only speculating, but since Tanizaki was one of the authors heavily influenced by the West, he maybe came across the name Naomi somewhere and thought "oh, this is a western name, but it could also be japanese". Else it would be weird how he descripted it as "if spelled in letters looks like a Westerner", that association must have come from somewhere.
(痴人の愛』のナオミを追加してみました。作中で「Naomiと書くと西洋人のよう」と書かれてあるので、作者はNaomiをある程度は知っている模様)

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So it could be that he chose Naomi because it sounded like "Naoko", but with an ending much less common, making Naomi the new "modern woman" with a name that was "like a Westener's", while "Naoko" would be the traditional one.

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Apparently he also spelled the name in Kanji as 奈緒美 and not with the typical 直 or 尚, and I'm not certain on this one, but I always felt that 奈 in names was also quite a modern character.

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Of course, the author using the name because of it having a double origin is also possible. To be certain one probably really has to research the creation procedure of the novel or find some record of Naomi as a name used before that date.

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Here is another wikipedia article, where they also list Naomi along with Risa or Erika as an originally foreign name that is today commonly considered a normal Japanese name.
http://ja.wikipedia.org/wiki/%E4%BA%BA%E5%90%8D