Aa- Prefix for Towards
aat - prefix for Ablative, e.g. sense of "from"
a - "a" and "aa" are ambiguous sounds in many languages and do not have 3 grades like other vowels, so 'Ram' in Sanskrit becomes 'Rama' in English, but in Sanskrit 'Ramaa' is Feminine version of Ram, like 'Krishn' becomes 'Kirshna' but 'Krishnaa' is Feminine of 'Krishn'. My children even today, after years of training in Hindi and Sanskrit, still have tendency to pronounce "aa" sound as "a" or "o" and when "a" sound is built into the consonants, like English, add an additional 'a', which makes it 'aa' sound.
'up' - prefix for 'away' - towards an object.
'paay' - obtainable - from root 'paa', and when someone adds "aaya" it can becomes "Potential Participle", something that should happen or be done, and this can also come as "Gerun", something indicates a sense of being completed, but it falls more in the category of "Preposition" or "Adverb", indicating "before-ness" or "a manner of verb occurance", and for verbs with prefix usage, "aay".
'iya' - ending for making an 'adjective' with 'ness' in mind - indicating an attribute possession. The 'a' comes because of "ambiguity of 'a' sound.
So the meaning is "A name which goes away or comes from the object, as a means towards obtaining the object-ness".
Basically a name that itself describes the object and comes from the object itself! A paradox, but here the paradoxical object is nothing but a natural sound one finds in the nature.
"Upaaya" in Sanskrit means "Method" with the same context.
like a scooter in Hindi is called "Phat-Phati" because it makes that sound of "Phat-Phat".