How did the Byzantine Empire named the Mediterranean Sea?

The Oxford Dictionary of Byzantium confirms John Bard’s answer:

As late as the 4th C., the Mediterranean continued to be an “inner sea,” totally surrounded by the territory of the Roman Empire. It was the only sea for Greeks, the esō thalassa [internal sea] (Aristotle) as opposed to the exō thalassa [external sea] or ocean; for the Latins the mare internum, intestinum, or nostrum. The term mare mediterraneum did not appear until the 3rd C.; Isidore of Seville used it in the early 7th C. (O. Maull. RE 15 [1932] 2222). The Byz. did not have a general term for the Mediterranean, although they used special names for its parts—the Aegean, Ionian, Tyrsenikon (or Tyrrhenian), Sikelikon, Kretikon pelagos [sea].