I frequently attend Japanese language classes, so I can definitely help you with this.
With the western pronounciation of
Naomi, the first and second syllables are slightly run together to create the pronounciation of "na-YOE-mi". In Japanese, the running-together doesn't happen, making the pronounciation "na-Oh-mi". The "oh" sound is like the "o" in "old".
Hope this makes sense! If it doesn't, let me know and I'll try and explain it in more simple terms.