Actually, both aYana and aYAna (as well as AYana and AYAna) have meanings in Sanskrit: the meanings are different. (the a close to the vowel in cut, Y as in yes, A as in car, n as in no). The one I have heard most commonly as a name is (http://www.behindthename.com/bb/arcview.php?id=312799&board=gen) aYana. Though the last a is dropped in many modern Indian languages, it is there in Sanskrit. In Sanskrit, the first syllable (the first a) bore the intrinsic (i.e. when not overriden by context) stress, most modern Indian languages are unstressed.
The nature of the vowels have changed in the modern Indian languages. Thus, in Bengali, the word (meaning the celestial path of the sun and planets, i.e. the region occupied bu the signs of zodiac) is pronounced like the English word awe followed by the y followed by the English word own (i.e. the first a as in caught, the second as in cone, and the last is dropped). As a Bengali name, however, the last syllable is often pronounced as the English word on rather than own (i.e. awe-yawn, except the `i' sound is not heard at the beginning of yawn; in other words the two a-'s are very similar). It is often spelt Ayan rather than Ayana when writing in the Roman script.