Did King James write the Bible?

Did King James really have his name written in the Bible?

In fact, two etymological entries (in Etymonline.com) show that "James" is not from "Joshua", but from "Jacob":

masc. proper name, name of two disciples of Christ, end of 12c. Middle English colloquial language of late Latin Jacomus (Source of the old French James , Spanish Jaime , Italian Giacomo ), modified from Latin Jacobus (please refer Jacob ).

(Entry James)

The entry on Jacob adds:

masc. proper name, name of the Old Testament patriarch, son of Isaac and Rebecca and father of the founders of the twelve tribes, from the late Latin Iacobus , from the Greek Jacobus , from the Hebrew Ya'aqobh , literally "one who takes by the heel" (Gen. xxviii: 12), a derivative of 'aqebh "heel".

When I look at the beginning of James' letter I see:

Ἰάκωβος Θεοῦ καὶ Κυρίου Ἰησοῦ Χριστοῦ δοῦλος ταῖς δώδεκα φυλαῖς ταῖς ἐν τῇ Διασπορᾷ χαίρειν.

that means (transliterated):

Iakobos Theou kai Kyriou Iesou Christou doulos tais dodeka phylais tais en te Diaspora khairein

Jacobus, a servant of God and the Lord Jesus Christ, to the twelve tribes scattered among the nations: Greetings.

It appears, therefore, that King James did not put his name in the Bible; he simply (taking transformations into account) had the same name as the (nominal) author of the letter.