What is the name of rabbit house?

Answer 1

If you are talking about wild rabbits they dig burrows that form underground "cities" called Warrens...If you are talking about domesticated rabbits they traditionally live in out door enclosers called a hutch.

However, house rabbits do much better living indoors than outdoors. You can build a great cage for much cheaper than buying one. Use shevling cubes, and cable ties (search cube cages on the web). Or using a expercise pen, that you'd use for a dog. they can be used in many different ways. Also, spaying and neutering will eliminate many "bad" behaviors, as well as reduce many health risks.