Noreen is a common name in the Americas, Ireland, Scotland, and the Middle East. Also spelt Naureen, Noirin and Nowrin (نوراني). In Arabic, the word means "luminous"'. In Ireland and Scotland, 'Noreen' is the anglicized version of 'Nóirín', which is the diminutive of 'Nora'.
Nazia is a name seen in both Pakistan and India, which derives from the word naaz, meaning pride. It may be difficult to introduce this name into the West, given the first four letters, which is unfortunate given its lovely meaning.