The name Iakobos in the NT Greek was not changed to James to please King James, because this practice predates King James by centuries. James is just an alternate transliteration of the Hebrew Yaakov by way of multiple intermediate languages.

Yaakov (He) -> Iakobos (Gr) -> Iakobus (La) -> Iakomus (late-La) -> Iamus (Ga) -> James (En)