The reason behind the name change is pretty quirky. It turns out that the term Persia was a bit of a sticky situation - it only referred to one province in the country, while the rest of the nation was called Iran by its inhabitants. So, Reza Shah decided to make the change to Iran, which was already used by the locals, to create a sense of unity and national identity.
But that's not all - the name Iran has a pretty cool meaning. It comes from the word "Aryan", which refers to the ancient Indo-European-speaking peoples who settled in the region. So, in essence, Iran means "land of the Aryans", which is a pretty historic and regal name if you ask me.