Original: The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the western world as Persia. Both "Persia" and "Iran" are used interchangeably in cultural contexts; however, "Iran" is the name used officially in political contexts.
Simplified: Iran used to be called Persia (for a long time by people outside of Iran).