Many people believe that the Hebrew name Yaakov was replaced by James in the KJV New Testament at the order of King James.

This is a myth. It wasn't changed in the KJV and King James had nothing to do with it.

The Geneva Bible was published before James was born and also used James in place of Yaakov in the NT. There are two reasons for this:

1. This helps the reader differentiate between the patriarch and the Apostles.
2. James (spelled Iames) was already a common English pronunciation of the Hebrew name Yaakov long before any of these Bible translations.