Again I am not saying dont call it IR of Pakistan or Pakistan. The Islamic identity is central to Pakistan. However be careful not to give one group too much sway on the affairs of governance. Strike a balance so all parties moderate each other. Swaying to either side of the pendulum will never benefit Pakistan or any other nation. It is a central rule of human history.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?
“You are free; you are free to go to your temples. You are free to go to your mosques or to any other places of worship in this State of Pakistan. You may belong to any religion, caste or creed—that has nothing to do with the business of the state.”
― Muhammad Ali Jinnah
“The great majority of us are Muslims. We follow the teachings of the Prophet Mohammed (may peace be upon him). We are members of the brotherhood of Islam in which all are equal in rights, dignity and self-respect. Consequently, we have a special and a very deep sense of unity. But make no mistake: Pakistan is not a theocracy or anything like it.”
― Muhammad Ali Jinnah