Why does Genesis 1 refer to God exclusively by the Hebrew title Elohim, "God," while the second chapter of Genesis, beginning in the second half of Genesis 2:4, speaks exclusively of Yahweh Elohim, that is, "the LORD God"? So striking is this divergence of the divine names that it has been common in critical circles of biblical scholarship to conclude that the writer, or, as those in the critical school prefer, the redactor (a sort of copyeditor) used basically two different sources for the two creation accounts found in the two chapters.

The person who paved the way for this theory of dual sources was Jean Astruc (1684-1766), the personal physician to Louis XV and a professor on the medical faculty of the University of Paris. While he still held to the Mosaic authorship of all of the Pentateuch, his volume on the book of Genesis published in 1753 offered the major clue that the names Elohim and Yahweh were the telltale traces that Moses used two sources to compose this material - material that obviously recorded events occurring before his time.

This explanation as to how Moses had access to material far beyond his own lifetime and the reason for the use of the dual names, however, was too facile; it failed to note that the variation in the employment of these two divine names in the book of Genesis was subject to certain rules that could be described rather precisely. First of all, the name Yahweh, "LORD," (notice the English translation convention of rendering this name in large and small capital letters, as opposed to "Lord," which renders another word meaning something like "master") is a proper noun used exclusively of the God of Israel. Elohim, on the other hand, is a generic term for "God" or "gods" that only subsequently became a proper name.

Yahweh is used wherever the Bible stresses God's personal relationship with his people and the ethical aspect of his nature. Elohim, on the other hand, refers to God as the Creator of the whole universe of people and things, and especially of the material world: he was the ruler of nature, the source of all life. This variation of divine names can be seen most dramatically in texts like Psalm 19. In this psalm Elohim is used in the first part, which describes God's work in creation and his relationship to the material world. But in the middle of the psalm the psalmist switches to the topic of the law of the LORD and the relationship the LORD has with those who know him; there the name Yahweh appears.

A further complication occurs because Exodus 6:3 notes that God says, "I appeared to Abraham, to Isaac and to Jacob as God Almighty, but by my name the LORD I did not make myself known to them." The resolution to this apparent contradiction to some 150 uses of the name Yahweh during the patriarchal period is to be found in a technical point of Hebrew grammar, known as beth essentiae, in the phrase "by my name." This phrase meant that while Abraham, Isaac and Jacob heard and used the name Yahweh, it was only in Moses' day that the realization of the character, nature and essence of what that name meant became clear. "By the name" is better translated "in the character [or nature] of Yahweh [was I not known]."

Thus the name Yahwoh is used when the Bible wishes to present the personal character of God and his direct relationship with those human beings who have a special association with him. Contrariwise, Elohim occurs when the Scriptures are referring to God as a transcendent Being who is the author of the material world, yet One who stands above it. Elohim conveys the more philosophically oriented concept that connects deity with the existence of the world and humanity. But for those who seek the more direct, personal and ethically oriented view of God, the term Yahweh was more appropriate.

Accordingly, Genesis 1 correctly used the name Elohim, for God's role as Creator of the whole universe and of all living things and all mortals is what the chapter teaches. The subject narrows immediately in Genesis 2-3, however; there it describes God's very intimate and personal relationship with the first human pair, Adam and Eve. God is depicted as walking and talking with Adam in the Garden of Eden. Therefore Yahweh is appropriately joined to Elohim to indicate that the Elohim of all creation is now the Yahweh who is intimately concerned to maintain a personal relationship with those who will walk and talk with him.

The above text is from pages 87-88 in the excellent book