It was indeed originally called the Persian Gulf by the Persians.
The term Arabian Gulf really just arose within the past 100 years as part of the pan-Arab and Arab nationalist movements when the Arabs were helping the British defeat the Ottoman Empire during WWI.
The primary name is definately Persian Gulf. I believe also that Arabian Gulf is also a recognized name now, but a secondary name.
From the impression I get National Geographic didn't do anything wrong. They clearly pointed out that Persian Gulf is the primary name with Arabian Gulf displayed below it in paranthesis.
If you read the article, Iranians are also angry at the fact National Geographic designated the Abu Musa and Lesser & Greater Tunb Islands as "Occupied by Iran and claimed by the United Arab Emirates" which is entirely correct.
Abu Musa and the Lesser & Greater Tunb Islands are indeed part of the United Arab Emirates and were invaded by Mohammed Reza Shah Pahlavi in 1971.
The Arab League (the twenty-two Arab states) has been demanding that Iran pull out of these three islands, but Iran has refused.
The islands are rich in oil resources which is why they won't pull out. Following the Islamic revolution in 1979, Ayatollah Khomeini's government wanted to improve relations with the Arab countries which had been severed by the bullish Mohammed Reza Shah Pahlavi government. However, when the very rich oil resources were discovered, they decided not to pull out.
This is why relations between the Arab countries and Iran are not very good. But they won't go to war over these islands.
"Generosity is giving more than you can, and pride is taking less than you need." - Khalil Gibran