I can see where this could get confusing. The name used on Herod was the name used on the latest version of James SoZ (which was just "James" in the I deck).
We do have some precedence for 'only refers to the person intended' (see NT Joseph vs OT Joseph, EC Salome vs Hero Salome, etc.). The 'any name of similar' only applies when something actually references the same person (King David and David, Sanhedrin and The Sanhedrin, etc.), so that does not apply.
Therefore, I would rule that this only refers to James, Son of Zebedee, since that is who Herod Agrippa I killed (and the verse only references him as "James brother of John"). I would similarly rule that only cards referencing James, Son of Zebedee could be targeted, and not cards of similar name (like James, Son of Alphaeus).
