I am reading Cases in International Relations by Donald M. Snow. There is a sentence as follows "The major theme and goal of the Shah’s rule was the restoration of Iran—the Peacock Empire—to its former glory among the countries of the world." The Shah was Muhammed Reza Pahlavi. I did not find much while searching online and any help is appreciated. Thank you.
The name stems from a famous golden throne called the Peacock Throne.
Originally the throne was commissioned by Mughal ruler Shah Jahan (the guy who also had the Taj Mahal built) for the Red Fort in Delhi. He wanted a way to publically display all the gold and the precious gems and pearls in his treasury without being weighted down by it. It was a really extravagant piece and twice as expensive as the Taj Mahal. It was finished in 1635 and remained a fixture of Mughal live for over 100 years.
The throne was originally just called the golden throne, but got his name at a later date from the peacock decorations on it.
In 1739 the Persian King Nader Shah sacked Delhi and captured the throne.
He continued to rule parts of the former Mughal empire and became the next person to "sit on the peacock throne". Sitting on it was one way of declaring rule over the land he had captured.
The original throne was lost in 1747, but ever since 1739, the throne of Persia/Iran has been called "the peacock throne".
Additionally there is also a legendary bird called huma or homa in Farsi, it is the symbol of Iran Air.
There is some superficial association of peacock = homa, so calling the throne "peacock throne" gave the ruler more status. The Melek Taus of Yazidi religion probably also came into play.
From the throne the name then trickled down to Iran/Persia itself. From mid-19th century on you can find references to Iran as "peacock empire".