I am currently searching for more information. "Middle-Earth" is apparently also used to refer to all the lands within the Outer Sea, including Valinor. I'll update the answer later today.
"Middle-Earth" is the continent between the West and East Seas
It is created after the destruction of the Pillars and although its shape changes over the ages, the whole continent is always named "Middle-Earth".
Before Middle-Earth
Prior to the destruction of the Pillars, "Middle-Earth" does not exist: there are no seas and therefore no "land in the middle". The Valar dwell on the Isle of Almaren, in the middle of the Great Lake. I could find no name for this land except The Kingdom of Arda.
Map of Arda before the destruction of the Pillars, The Atlas of Middle-Earth, p. 2
Creation of the continent
After the Pillars are destroyed, the West and East Seas are created, surrounding a large continent named "Middle-Earth", or Endor. It is located between Aman in the West and the Lands of the Sun in the East. This definition never changes, although the shape of the continent changes over time.
ibid.
The Second Great Battle
This particular geography would only last until the Elves are discovered and the Valar fight the Second Great Battle against Melkor. After the battle, several regions are now defined within the continent, such as Beleriand in the Northwest, Palisor in the East and the Hither Lands in the South. These are merely subdivisions of the continent, still named Middle-Earth.
Map of Arda after the Second Great Battle, The Atlas of Middle-Earth, pp. 4-5
Note that the Dark Lands appeared after the Second Great Battle, not as part as the destruction of the Lamps.
The War of Wrath
The next major change in geography is at the end of the First Age, during the War of Wrath, when a large chunk of the Westernmost part of Middle-Earth (Beleriand) is completely destroyed and the island of Númenor appears.
Map of Arda after the War of Warth, at the beginning of the Second Age, The Atlas of Middle-Earth, pp. 38-39
The Akallabêth
Finally, near the end of the Second Age, Arda becomes round instead of flat and the island of Númenor is destroyed, but this event does not significantly change the geography of the continent.