complete names...

(An aside: The complete names of the Indian notation are as follows: Shadjam for Sa, Rishabham for ri, Gandhaaram for ga, Madhyamam for Ma, Panchamam for pa, Dhaivatam for dha and Nishaadham for ni - This information is provided just so that you don't get too zapped when someone uses these full names)
Even in case of Indian music, we can extend our labeling of the keys to other octaves, much like in the Western system. In Indian music, the main octave is called 'Madhya stayi', the octave above it (higher) is called 'tara stayi' and the octave just below the Madhya stayi is called 'Mandra stayi' (based on the way 'mantras' were chanted in low frequencies in the centuries past). In terms of notation, the keys in the higher octave are labeled with a dot on TOP of the notes. The keys in the Mandra (lower) stayi are identified with dots BELOW the solfege notes.
Many good Indian musicians have voices spanning the entire three octaves, although most Indian compositions use up just the complete Madhya stayi scale and the top half of the Mandra stayi (only half an octave below) and the bottom half of the Tara stayi (just half an octave above the Madhya stayi).
We also see that the twelve keys of the octave divide into two halves. The four keys which are designated as ri and ga are called the 'bottom tetrachord' (in Indian terminology, 'Poorvaangam') and similarly the four keys corresponding to dha and ni are called the 'upper tetrachord' or 'Uttaraangam'. There is some kind of a symmetry between the bottom and the top tetrachords and key label assignment.
Just when you thought you had seen enough of the buzzwords, here is one more ! The starting frequency of your personalized octave relative to a 'standard' octave determines the 'pitch' of your voice. Your signature 'pitch' or 'sruti' (here we are using the word 'sruti' to mean 'the starting frequency of 'your' octave') is measured in a weird sounding unit called 'kattai'. Half a 'kattai' is a semitone and a full kattai is a 'whole tone'. If your octave happens to start at 240 Hz then you have a 'four kattai sruti', by definition. If your voice is very low pitched then you can have lower than four kattai as in case of many males. Women and children are high pitched and can have higher than four (even six) kattai srutis and their octave will start at frequencies higher than 240 Hz. An approximate Western equivalent of this is called 'Register'. In Indian classical music, the octaves are 'free floating', varying from person to person. The starting points are not pegged at 240 Hz.