The KJV is a different translation. Henry VIII preceded James I (see the quotes from the various articles below) and the KJV which is dedicated to him, is still in use today. Henry VIII authorized the "Great Bible".
Henry VIII:
"Henry VIII (28 June 1491 – 28 January 1547) was King of England from 21 April 1509 until his death. He was also Lord of Ireland (later King of Ireland) and claimant to the Kingdom of France. Henry was the second monarch of the House of Tudor, succeeding his father, Henry VII.
"Henry VIII was a significant figure in the history of the English monarchy. Although in the great part of his reign he brutally suppressed the Protestant reformation of the church, a movement having roots with John Wycliffe of the 14th century, he is more popularly known for his political struggles with Rome. These struggles ultimately led to his separating the Anglican church from the Roman hierarchy, the Dissolution of the Monasteries, and establishing himself as the Supreme Head of the Church of England. Although some claim he became a Protestant on his death-bed, he advocated Catholic ceremony and doctrine throughout his life. Royal backing of the English Reformation was left to his heirs, the devout Edward VI and the renowned Elizabeth I, whilst daughter Mary I temporarily reinstated papal authority over England. Henry also oversaw the legal union of England and Wales (see Laws in Wales Acts 1535–1542). He is noted for his six marriages."
Great Bible:
"The Great Bible was the first authorized edition of the Bible in English, authorized by King Henry VIII of England to be read aloud in the church services of the Church of England.
"The Great Bible was prepared by Myles Coverdale, working under commission of Sir Thomas Cromwell, Secretary to Henry VIII and Vicar General. In 1538, Cromwell directed the clergy to provide "one book of the bible of the largest volume in English, and the same set up in some convenient place within the said church that ye have care of, whereas your parishioners may most commodiously resort to the same and read it."
"Although called the Great Bible because of its large size, it is known by several other names as well: the Cromwell Bible, since Thomas Cromwell directed its publication; Whitchurch's Bible after its first English printer; also the Chained Bible, since it was chained in "some convenient place within the said church". It has also been termed less accurately Cranmer's Bible, since Thomas Cranmer's preface appeared only in the second edition."
James I:
James VI and I (19 June 1566 – 27 March 1625) was King of Scots as James VI, and King of England and King of Ireland as James I. He became king in Scotland as James VI from 24 July 1567, when he was only one year old, succeeding his mother Mary, Queen of Scots. Regents governed during his minority, which ended officially in 1578, though he did not gain full control of his government until 1581. On 24 March 1603, as James I, he succeeded the last Tudor monarch of England and Ireland, Elizabeth I, who died without issue. He then ruled England, Scotland and Ireland for 22 years, often using the title King of Great Britain, until his death at the age of 58.
KJV:
It should be noted that the KJV was dedicated to him (in 1608) per the wikipedia article. Also, "The Authorized King James Version is an English translation of the Christian Bible begun in 1604 and first published in 1611 by the Church of England. The Great Bible was the first "authorized version" issued by the Church of England in the reign of King Henry VIII. In January 1604, King James I of England convened the Hampton Court Conference where a new English version was conceived in response to the perceived problems of the earlier translations as detected by the Puritans, a faction within the Church of England."
Great Bible: First printing completed April 1539 (note that this is not the first English Bible). Last printing, 1569 (Thirty editions were printed).
"King James' Version: First printing completed in 1611.
There were at least three different translations/versions printed between the Great Bible and the King James Version. I've provided links to the various wikipedia articles and although these are not necessarily the final authority on the history, they do represent a good place to start.
Good Question. I think the only reason that James' name appears on the KJV is because it was dedicated to him... He certainly did not translate it.