I want to start off by acknowledging that this is tendentious speculation, but I cannot say for sure why it might be wrong, except that I cannot create a clear trajectory for this relationship.
Is the name Caspius/Caspi (the Caspian Sea, the Caspians) ultimately derived from a Semitic root? I came across the Akkadian word kaspum meaning "silver" and wondered if there was a connection. The root KSP is common across Semitic languages; cf. "Hebrew כֶּסֶף (kɛ́sɛp̄, “silver”), Classical Syriac ܟܣܦܐ (kespā) and Ugaritic 𐎋𐎒𐎔 (ksp kaspu)."1.
I don't believe that silver is associated with the Caspian Sea, but Etymonline does mention the possibility that the word is related to "white":
of or pertaining to the great inland sea of central Asia, 1580s, from Latin Caspius, from Greek Kaspios, named for native people who lived on its shores (but who were said to be originally from the Caucasus), Latin Caspii, from a native self-designation, perhaps literally "white." Middle English had Caspy, Capsi.
I'm not sure what led to this conclusion, but I do note that an area on the banks of the Caspian sea was called Albania.
Silver is often related to various words relating to white. The PIE *h₂erǵ- "shining, white" is the root for various words meaning "silver", including Latin argentum and the Sanskrit रजत (rajata). While this doesn't seem to be the case for the Semitic root KSP, it could be a case of an exonym placed on the sea by a Semitic-speaking population (Aramaic is the likely culprit, if any, since I don't believe the Akkadians, Assyrians, or Babylonians ruled that far north), which later obtained the associations that came with IE speakers, perhaps Scythians or other Iranian tribes?
I didn't see it in the Muss-Arnolt article mentioned by Jasper May here, though that doesn't mean others have considered it before.
Is the above hypothesis valid? If not, what major obstacle prevents it from being a possibility?