I believe it is called the middle ages because it comes between the Classical Period (the Fall Of Rome-476) and preceeds the Early Modern Period. It is the middle period of a 3 period division of Western History -Classical, Medieval, and Modern.

Middle ages (adjectival form) and Medieval is a periodization of European History.

The Middle ages came in three stages:
1. Early 500-1000
2. High 1000-1300
3. Late 1300-1500


Short answer. Hope it helps.

jmac