What is the name of the deep-ocean zone with no light at all?

The aphotic zone in general, and below about 4,000 metres the abyssal zone specifically - permanently dark, near freezing, under enormous pressure, and covering most of the sea floor. Sunlight is gone entirely by about 1,000 metres; below that the only light is made by the animals themselves.

And most of them do make it. Bioluminescence is thought to be present in the majority of species in the deep ocean, which makes it arguably the commonest form of communication on the planet. It is used to lure prey, to startle predators, to signal to mates, and in one strategy called the burglar alarm - an animal being attacked lights up conspicuously to attract something larger that will eat its attacker.

The food comes from above. Everything down there ultimately lives on marine snow, the continuous drift of dead plankton and faecal material sinking from the sunlit layer, which is why deep-sea animals tend to be slow, long-lived and opportunistic. The exceptions are hydrothermal vents, where communities run on chemosynthesis rather than sunlight at any remove - the only substantial ecosystem on Earth independent of the Sun, and one of the reasons Europa and Enceladus are taken seriously.