After 2000 BCE, the term used for the southern region was 'Babylonia'. This term refers to the southern part of Mesopotamia, which was the region located between the Tigris and Euphrates rivers in present-day Iraq.

Babylonia was an ancient civilization that emerged in the southern region of Mesopotamia after the fall of the Sumerian city-states. It was characterized by the rise of the city of Babylon as a major political and cultural center.

The significance of Babylonia in this time period can be attributed to several factors:

1. Hammurabi's Code: One of the most notable achievements of Babylonia was the establishment of Hammurabi's Code, a comprehensive set of laws that governed various aspects of life. This legal code provided a framework for justice and influenced later legal systems.

2. Babylonian Empire: Under the rule of Hammurabi and his successors, Babylonia expanded its influence and became a powerful empire. It conquered many neighboring territories and established a centralized administration.

3. Babylon as a cultural center: Babylon became a hub of cultural and intellectual activities during this period. It was known for its impressive architecture, such as the Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World. Babylonian scholars made significant contributions to various fields, including mathematics, astronomy, and literature.

4. Trade and commerce: Babylonia's location between the Tigris and Euphrates rivers made it a strategic center for trade and commerce. The region benefited from its access to waterways, which allowed for the transportation of goods and facilitated economic growth.

Overall, the term 'Babylonia' is used to describe the southern region after 2000 BCE because it signifies the rise of Babylon as a prominent city-state and the establishment of a powerful empire in the region. It represents a significant period in ancient Mesopotamian history marked by political, legal, cultural, and economic developments.