Say there are 3 people in the room. Each of them have a unique voice timbre. I want to recognize people by their timbre and know who's speaking.
The task of taking a long contiguous audio recording and splitting it up in chunks in which only one speaker is speaking - without any prior knowledge about the voice characteristics of each speaker - is called "Speaker diarization". You can find links to research code on the wikipedia page.
If you have prior recordings of each voice, and would rather do classification, this is a slightly different problem (Speaker recognition or Speaker identification). Software tools for that are available here (note that general purposes speech recognition packages like Sphinx or HTK are flexible enough to be coaxed into doing that).