In pre-Roman and early-Roman years, they called themselves Hellenes ("Greeks" is a complicated name, never used by Gre...Hellenes themselves, even today).

Later they called themselves Rhomaioi, which essentially meant "We're actually Hellenes, but the church calls us pagans, so we're Rhomaioi *wink*"

The term "Hellenes" was revived in the 15th century in an attempt to rouse rebellion against Ottoman occupiers and to re-assert Orthodox Christianity.