I've always thought of
Naomi as being pronounced nye-OH-mee (or nie-O-mee, same thing) and on the few occasions when I had reason to say the name (back when we had a cleaning lady with the name, as stated), that's how I said it. My entire family back then called her nye-OH-mee. That's what trips off my tongue. But just now out of curiosity, I asked three people who are in the room with me how they pronounce
Naomi and they all said nay-O-mee. Huh.
I think that nye-O-mee is prettier in any case.