This is because the naming comes from Chinese historiography, rather than the western one, and that is just how the Chinese name their political history. There is also the fact that unlike the "Byzantine Empire", "British Empire" or "German Empire", there's only one Chinese Empire, ruled by multiple dynasties who ruled the very same spot for more or less 3000 years in continuance, and then there's the relative longetivity of Chinese dynasties, and hence one dynasty can encompass periods up to 400 years, and each dynasty marks a very different geopolitical and cultural landscape, and such it is necessary to mark the history of the Chinese according to the dynasties, or more recently, the form of the republics.

Another fun fact, the name "Middle Kingdom" assigned to China is as old as the Chinese writings itself, which is more than 3000 years old, so calling China simply "Chinese Empire" in context of history can be extremely confusing.

Actually they are referred to as dynasties--the Tang Dynasty, Song Dynasty, etc., just as one refers to Komnenian dynasty--all defined by a familial succession of rulers, e.g. the house of Zhao for the Song. "Song Empire" is essentially a contraction of "the empire of the Song Dynasty." The Byzantine Empire on the other hand was made up of a succession of different ruling houses.