Persia as a word for the whole region is an exonym, derived of the name of a single province and the people who lived in it. Iran is the endonym that the people living in the area have understood to refer to the entire area for millennia.

It's like calling the Netherlands Holland. Everyone understands what you are talking about, but it is definitely not very precise, and some people from the region might take an exception to it. Fine for conversational use, not so much in academic literature. You might talk about the Persian Empire when referring to the Achaeminids or the Sassanids, but that comes with the understanding that while the ruling class is Persian, they rule over an empire of people, many of which are Iranian but not Persian.