The Persian civilization was one of the oldest civilizations in the world. They were the Persian empire but were conquered by the Greeks who took a beating from the Romans. Then Persia faded into obscurity until the country was renamed "Iran" and British companies began pumping oil.
The 50s onward
In our timeline, the 1952 coup put Iran on the path towards the 1979 revolution. This coup was the result of US intervention and the fear of Communism, two things which this timeline omits due to both of them being the direct result of WW1. Iran harbored resentment against the UK for sapping its oil reserves and so nationalized the oil industry. Germany was the country's largest consumer of oil products and befriended the country. Iran, being less far right than the rest of the Middle East, had much less Shariah law. The shah (king under limitations until OTL coup which made him absolute monarch) even tried to convince the king of Saudi Arabia to allow their women to wear skirts. The Iran-Iraq war never occurs as that was a result of the Iranian revolution. This does not, however, mean that the two countries don't have tensions as the Baathist regime was a threat to other Middle Eastern countries.
Iran is a mostly secular country (even though 90% of the country follows the Koran's teachings). Its military consists mostly of imported weapons from Germany (much of the middle east and the developing world imports their military goods). The country's government is a parliamentary democracy with a monarch figurehead much like Great Britain's government. There is no nuclear program controversy (though the country is building nuclear reactors) as the country is more open to inspection and is not suspected of developing nuclear weapons; Iraq is a different story. The population is smaller than the otl 79 million because in our timeline, the theocratic government encouraged higher birthrates to raise a bigger army (though the country is currently trying to curb it).