Off the top of my head, Syrians ("Phoenicians"), Greeks, Arabs, Armenians, and Persians and, considering they'd been ruled by Greeks (or the Greek-speaking half of the Roman Empire) for a thousand years, fairly high.

They still had local languages and cults, though, that kept a local feeling alive. This showed up in the schisms and heresies of early Christianity, where they identified with Nestorius and some of the Miaphysites against Rome, Constantinople, and Alexandria. Still have a separate church.

Some places to look if no one else helps you are the Roman Geographies like Strabo's that would go into some of the local customs and some of these articles at Google Scholar. If you did deep enough, though, you should find some weird things. The Byzantines practiced wholesale movements of peoples after wars as a method of control.