Persia is an exonym, but Greece and Egypt are also exonyms (Greeks and Greece was how Romans called them, not how they called themselves, while Egypt was the name used by Greeks, not by the natives of Egypt).

When talking about ancient people and countries, it is hard to avoid using exonyms, as they are usually much better known than whatever names may have been used by natives. In many cases such names have been discovered only relatively recently, during the last century, so they are known mostly by professionals and they are rarely found in popular literature. Moreover, frequently for the native names there is a much greater uncertainty about their original pronunciation than for exonyms.