Early Middle Ages is common, generally dating from "the fall of the Roman Empire" (which is itself a very ambiguous term) to around 1066.
The collapse of the Roman Empire from the 3rd to the 7th century (the process is somewhat more gradual than depicted in popular culture, and the timing depends on where you lived in the Roman Empire) resulted in a serious loss of administrative capability and economic and military coordination within the former empire. The only organization that remained for the Western Roman Empire was the Church, and even this was quite attenuated and didn't have the same reach the Roman Empire enjoyed at its height. The Carolingian dynasty did manage to piece together a successor empire that could have became a revival of the Roman Empire, but the succession practice of divvying up the lands between sons meant that the union didn't last long. On top of this, the Viking raids provoked a challenge that the nascent empires were unable to cope with.
The term Dark Ages arises from the very real decline of writing within Western Europe during this time, given that historians have historically been very biased towards surviving written accounts. Furthermore, for the Protestants in the Renaissance, the fact that the Catholic Church was the primary remaining artifact of Roman rule and therefore the dominant factor throughout most of this era caused them to emphasize the notion that nothing of cultural importance happened in this era, extending it to encompass the entire Medieval period until the Protestant Reformation and the Renaissance. In more recent historiography, the Dark Ages has been more compressed in time to encompass parts of Late Antiquity and Early Medieval, with the exact time period more dependent on which region you're talking about.