Yeah tbh it's a mostly weird idea to call the Roman Empire and Romans anything but Roman. Only half the country broke apart, a millennium and a half before the rest of it all did - so what if the first half to collapse contained the one-time capital that they got the name from. The Greeks spent like a thousand years as the imperial core of the Roman Empire, called Romans by everyone, and it doesn't take that long to update terminology. "Byzantine" was only used to describe Eastern Rome after it collapsed. They were still often called Roman until the 20th century, when the more popular Hellenes finally pushed it out completely, after becoming more and more popular for several centuries, as Roman had acquired a connotation of being politically subservient to the Ottoman Empire. For a while "romans" mostly referred to people from Istanbul.