The Russian ISS module that serves as the main living quarters is Zvezda. Its name means “star” in Russian, and the module is also formally known as the Zvezda Service Module.
Zvezda launched on a Proton-K rocket on 12 July 2000 and docked with the already orbiting Zarya module on 26 July. It became the third major ISS element and supplied essential life-support, propulsion, communications, power-distribution, and flight-control functions during the station’s early years.
The module contains crew sleeping quarters, a galley, exercise equipment, hygiene facilities, and systems for managing oxygen and carbon dioxide. Two dedicated sleep stations are located in Zvezda, although later modules expanded the station’s overall accommodation.
Poisk is primarily a docking and research module, Nauka is a laboratory and service module, and Zarya was the first ISS module and an early control and propulsion element. Those names are therefore plausible distractors, but Zvezda is the canonical answer for the Russian living-quarters module.