Tenny Frank - Race Mixture in the Roman Empire - The American Historical Review, 1895. It is important to notice that this is about the early pre-christian Roman Empire, not the period when the Roman Empire was governed from Byzantium.
As you can read in the article the Slaves of the ancient Romans came from almost everywhere e.g. Greece, Africa, Germany, etc. Tenney Frank tells that there seems to be very little overlapping between the surnames of the free-plebeians and the Slaves of the Roman Empire.
Tenney Franks (1916) writes for instance the following:
"To discover some new light upon these fundamental
questions of Roman history .... It has at
least convinced me that Juvenal and Tacitus were not exaggerating.
It is probable that when these men wrote a very small percentage of
the free plebeians on the streets of Rome could prove unmixed
Italian descent. By far the larger part - perhaps ninety per cent -
had Oriental blood in their veins".
Ancient Rome: Plebeian Council
Tenny Frank - Race Mixture in the Roman Empire - The American Historical Review, 1895