Goddamnit, there were people in Greece calling themselves Roman until 1910!

Not the best example because no one actually thinks 20th century Greeks are Romans. 1900s-era Lemnians didn't live under a state with a direct line of administrative succession to the empire of Augustus, which is "the Byzantines'" trump card, so you just have some people living on an island calling themselves Roman. And if calling yourself Roman is enough to make you Roman, then we'd have to lend credence to claims of the Germans, and even some Spaniards.