Genesis 2:4 BDC: “God” is used in Genesis chapter 1, while chapter 2 changes to Jehovah God. Does this mean that there are two different authors of Genesis?

The higher critics argue that every Bible verse that contains the Hebrew word for God, (Elohim), set off by itself has its own writer, designated by the capital “E” (“Elohist”). On the other hand, any verse that contains the Tetragrammaton, (Jehovah, Yahweh), God’s personal name, is attributed to yet another writer, “J” (“Jawist”). (Cassuto, 18-21) Let us see how they explain this. The critics argue that “God” (Elohim) is restricted to use exclusively in the first chapter of Genesis (1:1–31) in relation to God’s creative activity and that starting in Genesis 2:4 through the end of the second chapter, we find God’s personal name.