Our 22 Shrutis are basically presice sounds within an Octave (Saptak). Sounds are a natural phenomena and cannot be 'owned' by anybody.
Hence, our Shrutis which form the foundation of Indian Classical Music, do have 'Western' recognition and also names as below.
The Western names come from whether the tone belonged to the Just Intonation or Pythagorean or any other known scale.
Becoming conversant with this terminology will help us to interact with Western musicians and to explain to them the positions of our 22 Shrutis. (Refer to following table)