This name gives me an impression of a crabby middle aged women. (no offense) Anybody named Norene, I'm sure you're probably a nice person but yikes! Beware.
I really would consider this name as a substitute for the name Nora. Most people use Noreen but this spelling is preferred in my opinion. The combination of Norene Elinor is what I was thinking about. My grandmother's name was Nore Elinor so it would match without being exact you know? This is a great name! I see people named Norene as probably being humble and kind hearts.