Why is Persia now called Iran?

For the last 2600 years, up to the year 1935, following a naming convention that was started by the ancient Greeks, in all Western languages today’s Iran was known as "Persia", a word that was different from the word used in Persian, which was always “Iran”.

The leader of Iran in 1935 requested that the world refer to "Persia" by its native language. Hence, "Iran" is why we refer to that country as "Iran" and not "Persia." Very interesting history.

The people who live there like it better that way.

I expect its a result of their being invaded by Muslims in their past (they weren't a muslim country before, they had their own religion)