The former name of Iran was Persia. By western countries; Iran was formerly known as Persia. In the year 1935, Reza Shah Pahlavi, the Shah of Iran, emphasized the usage of the name Iran, and made sure that in all the official affairs the same name was used. As a result, population of Iran is addressed as Iranian instead of Persian. Although, in the year 1959, the government of Iran declared that both names could be used.
It is quite strange that the rest of the world knew the country as Persia prior to 1935, while the Iranians themselves referred to their country as Aryānām. According to historians, this referral was made from 1000 BC. However, there are no clear indications as what people of Iran actually called their country before that during the earlier dynastic rules. However, during Sassinad dynasty, the people used to call their country Iran, which literally means the Land of the Aryans.
When World War II was going on, Iran as well as Iraq, its neighboring country, was involved in the war. Both countries were occupied by the Allied forces. So, the names Iran and Iraq were commonly being confused. Therefore, the American government requested the Iranian government to continue using the name Persia at the UN to avoid this confusion. However, the US used the name Iran as it did not have much to do with Iraq in those times.