Yes, it is regional. Avani as a girl's name? Which part of India was she from? The word is very old and feminine meaning a stream bed etc., but only the meaning of `earth' survived. In Bengal, it forms the first part of various boys' names and these names are often shortened to merely avani. In that context it is pronounced awe-bony (as the two words juxtaposed). I think the previous poster's oven-ee came from that source. I do not know any part of India where oven-ee (as I would pronounce oven) is actually heard.
In Hindi India, the pronounciation should be avanI, where the v is less aspirated than in English (i.e. closer to w in the amount of breath). The last i is long (or could be short without change of meaning), and the two a's are close to the vowel u in English cut. The stress on the middle syllable in ancient Sanskrit can rarely be heard today.
India is a big country ... for pronounciation, the language they are speaking does matter. It would be less confusing to remember people not merely as Indians, but by their language and ethnicity. After all, I can clearly hear differences in pronounciations of the French and the German, and try to remember who is of which ethnicity, rather than remembering them merely as Europeans :-)