Why did Persia become Iran?
The native name of the region is Iran. The name Persia, comes from the Greeks, and so it is common in western countries to call the ancient Iranian Empire, Persia. Either name is acceptable in naming the modern nation.
Persia and Iran are the same country. Iran used to be called Persia, but has changed its name to Iran in modern times. Although, people still call Iran, Persia occasionally. And the story 'Arabian Nights' is the Western World's name for the story 'One Thousand and One Nights' which does take place in Persia (present-day Iran).