Is there a reason why the Hebrew word for silver is the same word for money in Hebrew?
Your assumption is not correct based on This article. See the 2nd paragraph.
In this week’s parshah (Breishit 31:30), Lavan says to Yakov: nichsof nichsafta le-veit avicha—you longed for your father’s house. The two words nichsof and nichsafta are both from the root KSF, the same room as KSF, money.
Most likely, the verb KSF originally meant “to become pale with longing.” And the noun KSF did not originally mean “money.” Rather, it meant “silver.” Why did silver get this name? Because of its whiteness, it became known as the “pale metal.” So the commonality between “silver” and “longing” is the whiteness/paleness aspect, and not anything else. I followed Ernest Klein: “A Comprehensive Etymological Dictionary of the Hebrew Language,” p. 282
Another widely used etymology book, “Etymological Dictionary of Biblical Hebrew” by Matityahu Clark, takes a slightly different approach. It views the fundamental meaning of KSF as “yearn, desire” and then views silver as a “desired asset.” But why should only silver be desired, why not gold? And why are not all precious metals called kesef? The better approach is the one taken by Klein, which focuses on the paleness aspect.
Later on, the word became to mean "money", but that's not its original meaning. Languages change for various reasons, and I suspect that since silver was originally used as a means to conduct business transactions, it was thought of as "currency" until paper notes and other metals were substituted.