As a historical dynasty, 东晋 isn't used in everyday casual conversation. Its usage is almost entirely restricted to specific contexts.
Historical and Academic Discussion: This is the primary context. Historians, students, and enthusiasts will use the term when discussing the Six Dynasties period. “In my lecture today, we will cover the political structure of the 东晋.”
Art and Museums: Art historians and museum curators frequently reference the dynasty. You will see 东晋 on placards describing pottery, paintings, and especially calligraphy from the era. “This artifact is a classic example of 东晋 celadon porcelain.”
TV, Film, and Literature: The Eastern Jin is a popular setting for historical dramas (电视剧) and novels. Its mix of political intrigue, aristocratic romance, and philosophical escapism makes for compelling stories. People might say, “I'm watching a new drama set in the 东晋.”
Metaphorical Reference: The story of the Eastern Jin, particularly the “gentry crossing south,” is a powerful cultural touchstone for migration and the preservation of culture in the face of disaster. It can be subtly referenced when discussing other major historical flights, like the one to Taiwan in 1949.