||The title of this article is a conjecture.
Though the topic is found within The Simpsons universe, a proper name is not available.
Apu's apartment is where Apu, Manjula their eight children live.
When the Octuplets were first born, they were given lots of free stuff as they were so popular in the media. Once the story that a couple in Shelbyville had nine children, all this stuff was taken away. When Homer and Marge turned up, Apu tried to give them a child here until they learned to cope with the children.
The apartment is part of a large block of apartments. It is decorated to look like an Indian house, since it has Indian-style doors and many other pieces of Indian furniture, including a Ganesha statue.