I was in Greece a few days ago and the tour guide called it by the above name, separate from the Byzantine Empire.
Is this common from Greek historians? Is there any substance behind this claim?
Not in my experience. A common term is 'the Greco-Roman world', which is employed when discussing cultural stuff (for example, "Homer was the preeminent poet in the Greco-Roman world"), but 'Greek-Roman Empire' would imply that the Mediterranean Roman-led hegemony was some kind of mutually arranged joint-enterprise, which is false, since the Romans subjugated the Greek mainland and wider 'Hellenistic kingdoms' with varying degrees of force.
However, the term has been used to describe the Byzantine Empire as a 'Greek Roman Empire' by some scholars, but not as the Greek Roman Empire, if you can see the distinction.
Further reading: