In the Western world, Persia (or one of its cognates) was historically the common name for Iran. On the Nowruz of 1935, Reza Shah Pahlavi asked foreign delegates to use the term Iran, the endonym of the country, in formal correspondence. Since then, in the Western World, the use of the word "Iran" has become more common. This also changed the usage of the terms for Iranian nationality, and the common adjective for citizens of Iran changed from "Persian" to "Iranian". In 1959, the government of Mohammad Reza Shah Pahlavi, Reza Shah Pahlavi's son, announced that both "Persia" and "Iran" could officially be used interchangeably. However the issue is still debated today.
The Modern Persian word Īrān (ایران) derives immediately from Middle Persian Ērān (Pahlavi spelling: ʼyrʼn), first attested in an inscription that accompanies the investiture relief of the first Sassanid king Ardashir I at Naqsh-e Rustam. In this inscription, the king's Middle Persian appellation is ardašīr šāhān šāh ērān while in the Parthian language inscription that accompanies the Middle Persian one the king is titled ardašīr šāhān šāh aryān (Pahlavi: ... ʼryʼn) both meaning king of kings of Iranians.
The gentilic ēr- and ary- in ērān and aryān derives from Old Iranian *arya- (Old Persian airya-, Avestan airiia-, etc.), meaning "Aryan", in the sense of "of the Iranians". This term is attested as an ethnic designator in Achaemenid inscriptions and in Zoroastrianism's Avesta tradition,[n 1] and it seems "very likely" that in Ardashir's inscription ērān still retained this meaning, denoting the people rather than the empire.
Notwithstanding this inscriptional use of ērān to refer to the Iranian peoples, the use of ērān to refer to the empire (and the antonymic anērān to refer to the Roman territories) is also attested by the early Sassanid period. Both ērān and anērān appear in 3rd century calendrical text written by Mani. In an inscription of Ardashir's son and immediate successor, Shapur I "apparently includes in Ērān regions such as Armenia and the Caucasus which were not inhabited predominantly by Iranians". In Kartir's inscriptions (written thirty years after Shapur's), the high priest includes the same regions (together with Georgia, Albania, Syria and the Pontus) in his list of provinces of the antonymic Anērān. Ērān also features in the names of the towns founded by Sassanid dynasts, for instance in Ērān-xwarrah-šābuhr "Glory of Ērān (of) Shapur". It also appears in the titles of government officers, such as in Ērān-āmārgar "Accountant-General (of) Ērān" or Ērān-dibirbed "Chief Scribe (of) Ērān".
The Greeks (who had previously tended to use names related to "Median") began to use adjectives such as Pérsēs (Πέρσης), Persikḗ (Περσική) or Persís (Περσίς) in the fifth century BC to refer to Cyrus the Great's empire (a word understood to mean "country"). Such words were taken from the Old Persian Pārsa – the name of the people from whom Cyrus the Great of the Achaemenid dynasty stemmed and over whom he first ruled (before he inherited or conquered other Iranian Kingdoms). Thus, the term Persian is an exonym and Iranians never historically referred to Iran by that exonym. The Pars tribe gave its name to the region where they lived (the modern day province is called Fars/Pars) but the province in ancient times was smaller than its current area. In Latin, the name for the whole empire was Persia, while the Iranians knew it as Iran or Iranshahr.
In the later parts of the Bible, where this kingdom is frequently mentioned (Books of Esther, Daniel, Ezra and Nehemiah), it is called Paras (Biblical Hebrew: פרס), or sometimes Paras u Madai (פרס ומדי), i.e. "Persia and Media". The Arabs used to likewise refer to Iran and the Persian (Sassanian) Empire as Al-Fāris (Arabic: الفارس), which would become the popular name for the region in Muslim literature.
The exonym Persia was the official name of Iran in the Western world before March 1935, but the Iranian people inside their country since the time of Zoroaster (probably circa 1000 BC), or even before, have called their country Arya, Iran, Iranshahr, Iranzamin (Land of Iran), Aryānām (the equivalent of Iran in the proto-Iranian language) or its equivalents. The term Arya has been used by the Iranian people, as well as by the rulers and emperors of Iran, from the time of the Avesta. Evidently from the time of the Sassanids (226–651 CE) Iranians have called it Iran, meaning "the land of Aryans" and Iranshahr. In Middle Persian sources, the name Arya and Iran is used for the pre-Sassanid Iranian empires as well as the Sassanid empire. As an example, the use of the name "Iran" for Achaemenids in the Middle Persian book of Arda Viraf refers to the invasion of Iran by Alexander the Great in 330 BC. The Proto-Iranian term for Iran is reconstructed as *Aryānām (the genitive plural of the word *Arya); the Avestan equivalent is Airyanem (as in Airyanem Vaejah). The internal preference for "Iran" was noted in some Western reference books (e.g. the Harmsworth Encyclopaedia, circa 1907, entry for Iran: "The name is now the official designation of Persia.") but for international purposes, Persia was the norm.
In the mid 1930s, the ruler of the country, Reza Shah Pahlavi, moved towards formalising the name Iran instead of Persia for all purposes. In the British House of Commons the move was reported upon by the United Kingdom Secretary of State for Foreign Affairs as follows:
On the 25th December  the Persian Ministry for Foreign Affairs addressed a circular memorandum to the Foreign Diplomatic Missions in Tehran requesting that the terms "Iran" and "Iranian" might be used in official correspondence and conversation as from the 21st March next instead, of the words "Persia" and "Persian" hitherto in current use. His Majesty's Minister in Tehran has been instructed to accede to this request.
The decree of Reza Shah Pahlavi affecting nomenclature duly took effect on 21 March 1935.
To avoid confusion between the two neighboring countries Iran and Iraq, which were both involved in WWII and occupied by the Allies, Winston Churchill requested from the Iranian government during the Teheran Conference for the old and distinct name "Persia to be used by the United Nations [i.e., the Allies] for the duration of the common War". His request was approved immediately by the Iranian Foreign Ministry. The American side, however, continued using Iran as it had at the time little involvement in Iraq to cause any such confusion.
In the summer of 1959, following concerns that the native name had, as one politician put it, "turned a known into an unknown", a committee was formed, led by noted scholar Ehsan Yarshater, to consider the issue again. They recommended a reversal of the 1935 decision, and Mohammad Reza Shah approved this. However, the implementation of the proposal was weak, simply allowing Persia and Iran to be used interchangeably. Nowadays both terms are common; Persia mostly in historical and cultural contexts, "Iran" mostly in political contexts.
In recent years most exhibitions of Persian history, culture and art in the world have used the exonym Persia (e.g., "Forgotten Empire; Ancient Persia", British Museum; "7000 Years of Persian Art", Vienna, Berlin; and "Persia; Thirty Centuries of Culture and Art", Amsterdam). In 2006, the largest collection of historical maps of Iran, entitled Historical Maps of Persia, was published in the Netherlands.
In the 1980s, Professor Ehsan Yarshater (editor of the Encyclopædia Iranica) started to publish articles on this matter (in both English and Persian) in Rahavard Quarterly, Pars Monthly, Iranian Studies Journal, etc. After him, a few Iranian scholars and researchers such as Prof. Kazem Abhary, and Prof. Jalal Matini followed the issue. Several times since then, Iranian magazines and Web sites have published articles from those who agree or disagree with usage of Persia and Persian in English.
It is the case in many countries that the country's native name is different from its international name (see Exonym), but for Persians and Iranians this issue has been very controversial. Main points on this matter:
There are many Iranians in the West who prefer Persia and Persian as the English names for the country and nationality, similar to the usage of La Perse/persan in French. According to Hooman Majd, the popularity of the term Persia among the Persian diaspora stems from the fact that "'Persia' connotes a glorious past they would like to be identified with, while 'Iran' since 1979 revolution... says nothing to the world but Islamic fundamentalism." 
Persian objects at Hermitage
Iran, or Persia as it was known in the West for most of its long history, has been mapped extensively for centuries but the absence of a good cartobibliography has often deterred scholars of its history and geography from making use of the many detailed maps that were produced. This is now available, prepared by Cyrus Alai who embarked on a lengthy investigation into the old maps of Persia, and visited major map collections and libraries in many countries ...
Persian Carpet, Cat, melon...