What is the name of place where rats live?

There isn't one specific name for a place where rats live. It depends on the context:

* If you're talking about their natural habitat: You might call it a burrow, nest, or den.

* If you're talking about an urban environment: You might call it a sewer, alley, or garbage dump.

* If you're talking about a place where rats are a problem: You might call it an infestation.

Ultimately, the best word to use depends on the specific situation and the tone you want to convey.