Excellent question, and the answer is: Several passages in Genesis reveal that YHWH (Yahweh) provided His Name:
Genesis 4: 26 And to Seth, to him also there was born a son; and he called his name Enosh. That is when people began to call upon the name of YHWH.
Genesis 12: 8 He (Avram) left that place, went to the hill east of Beit-El and pitched his tent. With Beit-El to the west and 'Ai to the east, he built an altar there and called on the name of YHWH.
Genesis 21: 33 Avraham planted a tamarisk tree in Be'er-Sheva, and there he called on the name of YHWH, the everlasting God.
YHWH's Name was never "God" or "ADONAI" or anything else; those were simply titles....
We are then told in Exodus that He provided His Name to Moses:
Exodus 3:13-15 Moshe said to God, "Look, when I appear before the people of Isra'el and say to them, 'The God of your ancestors has sent me to you'; and they ask me, 'What is his name?' what am I to tell them?" God said to Moshe, "Ehyeh Asher Ehyeh [I am/will be what I am/will be]," and added, "Here is what to say to the people of Isra'el: 'Ehyeh [I Am or I Will Be] has sent me to you.'" God said further to Moshe, "Say this to the people of Isra'el: 'Yud-Heh-Vav-Heh [ADONAI], the God of your fathers, the God of Avraham, the God of Yitz'chak and the God of Ya'akov, has sent me to you.'This is my name forever; this is how I am to be remembered generation after generation.
YHWH in Hebrew is comprised of the letters Yud-Hey-Vav-Hey: God Himself revealed His Name to us, and man has had acess to it all along. Ironically, traditional Jews refuse to utter his Name for fear of mispronouncing it or misspelling it, etc, and on the other end of the spectrum, you'll never hear the Father's Name in most Christian churches as they are all concentrating on "Jesus" whom they think came to replace the Father and abolish all his original Divine instructions/teachings....
The Aramaic English New Testament (AENT) (from which the contents of this article were borrowed) was a direct translation of the Khabouris Codex which was written in ALL Aramaic - and includes the correct Name of YHWH. The following explanation on the correct pronunciation of YHWH's Name was borrowed from an appendix in the AENT: