I've only ever seen
Neve pronounced NEEV, but if it was the Italian it could only be pronounced NEH-veh - 'eh' as in the 'e' in 'net' (Italian pronunciation is very specific!).
As for the origins, they are both equally valid - it is *either* an Anglicised spelling of
Niamh, *or* an Italian word-name meaning Snow. It's really up to the parent doing the naming - they decide whether they're giving the child the Anglo-Irish
Neve or the Italian
Neve, and pronounce it accordingly.
Any questions? :-)