Romans used to call the Mediterranean Sea "Our Sea", which has to do with the fact that the Roman Empire dominated the sea and controlled all the territories surrounding it. Starting from the 5th century, the empire gradually lost control of Hispania, Mauretania, and Africa. Eventually, the empire collapsed in the west, and none of the "Barbarian" states had control over the entire sea or could claim the entire coast. I wonder what did the Latin speaking population in the west ("Romans", so to speak) call the Mediterranean Sea after the "fall"?
From about the 7th Century, it began to be called "The Mediterranean Sea", meaning "the Sea in the middle of the world", in Late Latin.
Source:
http://www.etymonline.com/index.php?allowed_in_frame=0&search=mediterranean&searchmode=none