Persian Gulf is the most important sea in the Middle East. It is surrounded by seven Arab Countries and the only Persian country in the world which is Iran.
This sea is the key of the international stock markets since it is the major sea to transport the crude oil from the countries surrounding it.
People are free to call it the name they want, but to be fair, we must understand the history and the geography when we talk about such subject. people have different mentalities for understanding but facts are always the right witnesses in this regard.
From my point of view, I'd rather name it Arabian Gulf and NOT Persian Gulf.
But from other points of view, it is indeed the Persian Gulf, as generally accepted by the geographer's community.