Step 1: Understanding the Constitutional Provision
The question asks in whose name international treaties and agreements are formally signed by India. This relates to the executive powers of the head of state.
Step 2: Analyzing Executive Powers
In India's parliamentary system, the President is the formal head of the state and the head of the executive.
According to Article 77 of the Constitution, all executive actions of the Government of India shall be expressed to be taken in the name of the President.
This includes diplomatic functions. International treaties and agreements are negotiated by the government (led by the Prime Minister and the External Affairs Minister), but they are formally signed and ratified in the name of the President of India, who represents the nation.
Step 3: Evaluating the Options
(A) Prime Minister and (B) External Affairs Minister: They may lead the negotiations and even physically sign the documents, but they do so on behalf of, and in the name of, the President. They are the de facto authority, but the de jure authority in whose name it is done is the President.
(C) Home Minister: Deals with internal security and has no role in this.
(D) President: As the head of state, all international agreements are concluded in the name of the President.
Step 4: Final Answer
International treaties and agreements are signed on behalf of the President. Therefore, option (D) is the correct answer.