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.

Other such examples include confusing Monte Carlo for Monaco and saying Bohemia when talking about Czechia. During the cold war, the word Russia often got to stand in for the entirety of the Soviet Union.

> You might talk about the Persian Empire when referring to the Achaeminids or the Sassanids, but that comes with the understanding that while the ruling class is Persian

not exactly. Persians are also majority of people in what's now called Iran (just like Russians are majority in Russia, this is the same naming pattern as for many countries) and renaming is a result of an invasion. Talking about "ancient Iran" before it Muslims arrived is talking about Persia