Which animal's home is called a hive?

Bees, and a hive is closer to a single organism than a house. A colony holds a queen, tens of thousands of sterile female workers and a few hundred males, and no individual survives alone. Workers change jobs with age - cleaning, then nursing, then building, then guarding, then foraging in the last weeks of a six-week life.

The famous part is the language. A returning forager performs a waggle dance on the vertical comb, in the dark, and the direction of the waggle relative to straight up encodes the direction of the food relative to the sun, while the duration encodes distance. Karl von Frisch worked this out and shared a Nobel Prize for it; the claim that an insect uses a symbolic, abstract code was so unexpected that it was seriously disputed for decades afterwards.

Swarming is how a colony reproduces, and the decision-making is remarkable. Scouts inspect possible new homes and advertise them by dancing; a good site attracts more scouts, which dance for it in turn, and the swarm moves when a quorum is reached. It is a distributed vote with no one counting - and the colony reliably picks the best cavity available.