The significance of the various uses of the names Yahweh and Elohim can be better understood when we realise that often when the author uses the name Yahweh, the focus is on Judah, and whenever he uses the name Elohim, the focus tends to be on the northern kingdom of Israel. When the author uses the name Yahweh, he is speaking of an anthropomorphic God with human characteristics, made very clear in Genesis 3:8, where they heard the voice of God walking in the cool of the day. In these passages, Yahweh often made promises and covenants with his chosen people. When the author uses the name Elohim, people could never look at God, so he typically came in dreams or visions, but sometimes in the form of a cloud or a flame. This was a more transcendent God who required obedience and was feared by his people. The style differs, depending on which designation is being used.
All this points to at least two writers of Genesis, not one. In 1876/77 Julius Wellhausen, in Die Composition des Hexateuch und der historischen Bücher des Alten Testaments proposed what became known as the Documentary Hypothesis - that the Pentateuch was written by four different sources, three of which are found in the Book of Genesis. The Yahwist wrote down the traditions held in early Judah, while the Elohist wrote down the traditions held in early Israel. These were combined after the destruction of Israel in 722 BCE. The Priestly Source came much later than the Yahwist and the Elohist, sometimes using their designations, but quite often using El Shaddai as the designation for God. Subsequent scholars have challenged Wellhausen's hypothesis, but Mark S. Smith says in The Early History of God (page xxiii) that it has not been supplanted by a more persuasive model. Lester L. Grabbe, in Ancient Israel (page 44) says that many would still agree that Genesis was compiled mainly from three sources – the Yahwist (J), the Elohist (E) and the priestly writer (P), but opinion is now much more divided. Like Smith, he says that while the old consensus that had developed around the Documentary Hypothesis has gone, there is nothing to take its place.
Israel Finkelstein, in Archaeologies of the Middle East: Critical Perspectives, Archaeology, Bible, and the History of the Levant in the lron Age (p208ff), accepts the old Documentary Hypothesis as valid, and says that J (the Yahwist) deals first and foremost with the centrality and superiority of Judah over its neighbours - Israelites and non-Israelites alike. For reasons which stem from the study of archaeology, Finkelstein dates J to the seventh century BCE, later than the ninth-eighth centuries BCE date usually attributed to this source.
Scholars are working towards a more final explanation, but almost all agree that Genesis had more than one author.