What was the primary cause from the eastern roman empire to become what we think of as byzantine?

Well the east was never fully roman, they spoke greek and had a greek culture I'm not sure why they didn't keep the name but they felt it was right to switch it since they were never roman. Actually Rome conquered their lands and made them apart of the empire..

The statistics for the eastern war are grim. more than three-million men died in the fighting, more than nine-million men were wounded, and every major country which participated lost its form of government.