Sorry, that is not wher it came from.
It came from when certain nations ruled in power and the time periods from then
And that came from Daniel
Iron is older than than those time periods in history, but wwe dont call those earlier periods the IRON age, nor do we change Bronze or Iron around in those time periods when they were used at the same time.
The most common usage of iron age in science - and therefore, in archeology - refers to the system of the three-ages , introduced in the 1820s. It's neither based on the Ages of Men of the Greek mythology nor the Book of Daniel.
I have no idea what history books you read but there is no question that the use of metals is what gave the name to eras. Daniel had nothing to do with it since his model is even more vague that that you object to.