You do not mention who "they" are, so your question cannot be answered.
Speaking strictly in general terms, the names of executive positions that head a government can be:Prime Minister, Premier, Chairman, President, and King. Other titles may exist, however these are common ones.
The President is the the head of the executive branch.
The president is the head executive branch In the state.
The Governor of each state is the head of that state's executive branch.
The head of the Executive branch in a state is the Governor
The Governor is the nominal executive head of the state.The constitution vests the executive powers of the state to the Governor in India.
President is the head of the executive branch.
The Governor is the head executive in state government.
The head executive of the US government is the President, Barack Obama.
The head executive of the US government is the President, Barack Obama.
The head executive of a state government is called the Governor.
The head of the executive department could be called the Executive Department Head, supervisor, manager, etc.