I don't think we ever see this on TV. If we did, the TV-viewing audience would hear separate parties making separate queries more or less simultaneously, and it would be distracting for us, nevermind the computer.
Which brings me to my answer: it's possible that practicality and etiquette come into play. If someone is playing the radio at the beach, you don't set up next to them and play your radio. You either find another spot or learn to appreciate reggaeton. If you find a spot still within ear shot of the other people, but far away enough that your radio can drown out most of the other music, then you're good to go.
Although there are a variety of ways the computer can distinguish between different simultaneous speakers in the same area (frequency/pitch filtering, location sensors, relative volume, spoken language, syntax, artificial intelligence, etc.) it's also possible that it may just ask users to "Please restate the question."
One good example of the computer using context to figure out when to respond and when not to is from TNG: Schisms. But in that case they were working together and not talking all at once.
WORF: Computer, make the handle a single grip ten centimetres long, solid metal. Now make one blade longer, curved inward. And give the other blade a jagged edge. [Computer complies.]
TROI: All right, you were lying on the table. You had a bright light shining in your eyes. Were there any smells in the room? Were there
any sounds? [Computer is silent.]
RIKER: Yes. Yes, there was a sound. Computer, there were noises coming
from the darkness. Strange, like whispering. [Computer complies.]
KAMINER: More like clicks. Clicking sounds. [Computer complies.]
RIKER: Louder. Faster. More of them. [Computer complies.]