J.R.R. Tolkien calls the inhabited world of his mythology Arda.
Arda is the world that includes Middle-earth, Aman, and other lands in Tolkien’s legendarium. It was created within Eä, the wider universe brought into being by Ilúvatar, and its history is shaped by the actions of the Valar, the Maiar, Elves, Men, and other peoples.
Middle-earth is therefore not the name of the entire created world. It is one major region of Arda, especially central to The Hobbit and The Lord of the Rings. Aman, the land in the west, is another important part of the world’s geography.
Readers sometimes answer “Eä,” but Eä refers to the created universe rather than specifically to the world inhabited by the stories’ peoples. “Arda” is the precise term for Tolkien’s world itself.