According to the Watchtower, Eve was the first to use the name of Jehovah.
Watchtower-1959-October-1st-pp.591-592
“WHY DEATH?
27 What is the Bible’s biography of Adam? Why did Adam die? The Holy Scriptures definitely indicate that God wisely put a curb on man’s Edenic freedom by law. This legal curb was to remind Adam as a son of God that he was a dependent creature with a purpose to perform, the divine will, the will of his heavenly Father. This guidance of man’s life would bring man greatest happiness. God said to his son Adam: “From every tree of the garden you may eat to satisfaction. But as for the tree of the knowledge of good and bad you must not eat from it, for in the day you eat from it you will positively die.” (Gen. 2:16, 17) Eve and Adam defiantly rebelled against the Sovereign Power of heaven and thus disobeyed and sinned, and brought upon themselves this penalty of death, against which they had been warned. The Bible continues to say: “With that Jehovah God put him [Adam] out of the garden of Eden to cultivate the ground from which he had been taken. And so he drove the man out . . . Now Adam had intercourse with Eve his wife and she became pregnant. In time she gave birth to Cain and said: ‘I have acquired a man with the aid of Jehovah.’ Later she again gave birth, to his brother Abel. . . . And Adam lived on for a hundred and thirty years. Then he became father to a son in his likeness, in his image, and called his name Seth. And the days of Adam after his producing Seth came to be eight hundred years. Meanwhile he became father to sons and daughters. So all the days of Adam that he lived amounted to nine hundred and thirty years and he died.”—Gen. 3:23, 24; 4:1, 2; 5:3-5.
However, two year previous to the above quote in 1957 the Watchtower said, that it was in the days of Enosh when calling on the name “Jehovah” was started.
Watchtower-1957-April-15th-pp.234-235
“25 Because the first false god was his enemy and slanderer and had used a serpent to lead Eve and Adam into sin, Jehovah God called him “the dragon, the original serpent, who is the Devil and Satan.” (Rev. 20:2; 12:9, NW) Many of Adam’s grandchildren must have worshiped false gods. Many things that have to do with worship and that searching men have dug up from the earth from long ago serve to show that they did so. In the days of Adam’s grandson Enosh they even reached the point of calling other things by the name of Jehovah: “At that time a start was made of calling on the name of Jehovah.” (Gen. 4:25, 26, NW) False worship must have been speeded up when angelic sons of God in heaven disobediently came down from heaven by taking on the form of handsome men and marrying the good-looking women and raising children called Nephʹi·lim· “The Nephʹi·lim proved to be in the earth in those days, and also after that, when the sons of God continued to have relations with the daughters of men and they bore sons to them, they were the mighty ones who were of that world, the men of fame. Consequently Jehovah saw that the badness of man had become great in the earth and every inclination of the thoughts of his heart was only bad all the time.” What wonder that the earth was full of violence as a result of them! False worship always leads to that harmful result.—Gen. 6:1-5, 13, NW.”
Atlantis!