You can write a thesis - but when the Resolution of Pakistan in 1940 was passed - it did not say Islamic Republic of Pakistan. Nor when we gained independence it was IR of Pakistan. It was always Pakistan.
You don't have an understanding of why our country is officially the "Islamic Republic of Pakistan" because you don't understand the history behind the origin of our nations name.
For starters it was Chaudhary Rehmat Ali's "Now or Never" written in 1933 that introduced the name "Pakistan" but have you actually read his pamphlet and what he advocated for?
The term "Islamic Republic" is to denote that Pakistan was to be a constitutional democracy ruled in accordance with the Quran and Islamic principles.
For example Jinnah made it clear during his 1946 Address to the Students in Deccan:
“In Islam, the ultimate obedience belongs to God alone. The only way to follow His Guidance is through the Holy Qur'an. Islam does not preach obedience to a king, parliament, person or any institution. The Islamic government means Rule of the Qur'an. And how can you establish the Rule of the Qur'an without an independent state? In this state, legislation will take place within the boundaries drawn by the Qur'an.”
Jinnah further stated at the Darbar in Sibi, Balochistan on February 14, 1948:
“ . . . I have one underlying principle in mind, the principle of Muslim democracy. It is my belief that our salvation lies in following the golden rules of conduct set for us by our great law giver, the Prophet of Islam. Let us lay the foundation of our democracy on the basis of truly Islamic ideals and principles. Our Almighty has taught us that 'our decisions in the affairs of the State shall be guided by discussions and consultations'."
Jinnah, even during his final public speech, on April 18, 1948 (4 months before he died) to the students of Edwards College in Peshawar stated:
“I am happy to see better things here. What more can one really expect than to see that this mighty land has now been brought under a rule, which is Islamic, Muslim rule, as a sovereign independent State.”
This is why Pakistan is referred to as an "Islamic Republic".
What's difficult to understand about this?
Pakistan is more a Persian and Central Asian influenced than Arabic. The Saudi funded Maulvis, alonwith Zia's years, combined with JI and Mahdudi have built a completely warped sense of ourselves. So instead of us embracing our Steppes of Asia / Persian roots that inspired the Mughals and brought ghalib and sufis in our land, and gave us the glory of Indian subcontinent
Persian influences do exist due to its proximity to our peoples but our ancestry is not Persian nor does it originate from the Steepes of Asia.
Pakistan's civilization is A LOT older and grander than any of the regional empires that have developed over the course of history and our oldest connections aren't to Iran but Iraq formerly Mesopotamia which were our largest trading partners during the neolithic periods and many decades onward.
The Muslims of Pakistan and the wider Mughal Empire had much better relations with the Ottoman Empire than we ever did the Persians who were constantly attacking neighboring Muslim peoples both us and the Turks.