Byzantines or Romans never came close to controlling that area in any point in history. For most of history that area has was part of the Persian empire. He was only referred to Rumi because in latter parts of his life he traveled and eventually died in Western Asia (Anatolia) which is in modern day Turkey. However, before the arrival of the Turks it was known to the Persians and Arabs as Rum (Rome).
Byzantines or Romans never came close to controlling that area in any point in history. For most of history that area has was part of the Persian empire. He was only referred to Rumi because in latter parts of his life he traveled and eventually died in Western Asia (Anatolia) which is in modern day Turkey. However, before the arrival of the Turks it was known to the Persians and Arabs as Rum (Rome).