Identifying the sound of your own voice is so natural that no-one has hardly been concerned with the individual aspect of "voice" as yet. Speech and song is generated by our vocal cords. The same principle lies behind bringing human thought to expression.
In the most literary sense of the word "per-son-ality" (from Latin personare - to sound through) everyone has been assigned an individual being to whom corresponds a voice pattern that cannot be repeated - just like a fingerprint. A Dr. Vemu Mukunda from India was able to show in the 70s that voice is a sort of system for illustrating the human personality structure.