It is hard to prove unambiguously the path by which what we call Judaism was formed. The biblical evidence is that there were at least some monotheists in the Middle East before Abraham’s call. Job would be an example, and Abraham’s father Terah may have been a monotheist, as, perhaps, was Laban. The biblical account of the formation of Judaism is that it goes back to the historical person Abraham. Abraham was a very strong and devout monotheist who worshipped the one God who became the God of the nation of Israel. The Israelites struggled to throw off the polytheism of its neighbors for centuries, as is attested to in the Old Testament–especially in the prophets. However, monotheism remained the primary religious outlook of the descendants of Abraham. This was solidified when, through Moses, Israel was able to escape from slavery in Egypt. It was only at this late date–more than four hundred years after Abraham was given his promise of blessing from God–that the God of the Jews was first called YHWH (Yaweh). Before that, the God of the Jews was called El, Elohim, Adonai, and other names. Although the God of Israel was first called YHWH with Moses, the Israelite concept of God was not significantly changed with the receiving of the Law of Moses.
The idea that the Jews created their idea of God and borrowed his name from a Canaanite god Yaweh is not supported by good evidence. I found an article claiming that there was an Edomite god named Yaweh in the 13th century BC, but the evidence for this is slim at best. In fact, it is more likely that, if Yaweh was ever used as the name of a god among the Caananites, they borrowed the name from the Jews rather than vice versa. This possible Edomite god definitely postdates the use of YHWH by Moses. This theory from Wikipedia is speculation at best, and it flies in the face of the only direct evidence we have for the origin of YHWH, which is the Old Testament.
Most important to this question is not the origin of the proper name YHWH, but the origin of the monotheistic religion we call Judaism, which goes back to Abraham–long before the name YHWH was used.