If Zoroastrianism is so strong in Iran, why was there an Islamic revolution? Why is it proclaimed as the Islamic Republic of Iran?
There are only approximately 20,000 Zoroastrians in Iran, which is about 0.026% of the total population. I would not say Zoroastrianism is strong in Iran in terms of the total population. The only way Zoroastrianism can be said to be strong in Iran is because it has the second-largest Zoroastrian population after India (~69,000). See List of countries by Zoroastrian population.
Iran has a Muslim population of about 74,819,000 (figure from 2010), which is about 99.6% of the total population (Muslim Population by Country). Based on the overwhelming Muslim majority it is not difficult to see why it is proclaimed as the Islamic Republic of Iran.
Before Islam Iranians had problem with Zoroastrianism and were to an opportunity to get rid of t but Kings of Iran were Zoroastrians and this was not easy. It is interesting to know the last Zoroastrian King of Iran was killed by Iranians and not by Muslims. When Islam started some Iranians seeking truth went to Arabia to meet Muhammad PBUH and learn about Islam. The most famous of them was Salman Farsi the great companion of prophet. Farsi is Arabic form of Persian. And his name means the Solomon of Persia. Salman had great role in introducing Islam to Persians and converting them to Muslim. It can be said approximately that Persian inheritance is it dead and gone. Persian inheritance had no chance competing against powerful Islam inheritance.
Well, Zoroastrianism is not strong in Iran and has not been strong in Iran for the past 1300 plus years. The vast majority of Iran's population since the 700's CE, have been are are still, Shiite Muslims-(One could even say that Iran was the historical and contemporary Epicenter of Shiite Islam).
The Zoroastrian population in Iran proper is well below 1%. When Islam came to Persia/Iran 1300 plus years ago, a small percentage of Zoroastrians fled to India. The Parsi population within India are Persian/Iranian Zoroastrians.