Source theory attempts to rationalize Scripture to make it a work of man and not the Word of God. The question on how God writes about Himself is not a source of confusion when the text is seen in the light of the triune nature of God and the work of Jesus Christ in creation.
Genesis 1:1-2:3 relates creation from the beginning to the end of the seventh day using the word Elohim, a plural word. The only consistent explanation for using a plural word to describe a monotheistic God is the triune nature of God. In fact, it is illogical to promote the theory of human sources who describe a single God by choosing a plural word.
The second account identifies the Creator on a personal level as YHVH Elohim. All things were made through Jesus:
In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through Him, and without Him nothing was made that was made. (John 1:1-3 NKJV)
For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. (Colossians 1:16 NKJV)
The two accounts are saying the same thing in different ways. The focus of the first is creation in general ending with the blessing of the seventh day. The focus of the second is on the first man and woman which focuses on their personal Creator, YHVH Elohim; the rest of the Bible continues this dual message a single God with a triune nature and a personal redeemer, Jesus Christ.
There are several elements in the second account that point specifically to the work of Jesus Christ. First, the account starts on the third day:
This is the history of the heavens and the earth when they were created, in the day that the LORD God made the earth...Genesis 2:4 NKJV)
As the first account states the earth was completed on the third day, the beginning of the second only makes sense if read in the light of the first account: indicating a single source.
The second account starts on the third day, highlighting a 3-day period. The 3-day period also connects the next events which occur on the sixth day: the creation of the first man and woman. In other words, the period of time Jesus will spend in the earth after His crucifixion is the patterned after His work of creation. The two records are purposely structured to demonstrate the significance of 3-days and a personal connection to the Creator.
YHVH Elohim gives the command not to eat from the tree of the knowledge of good and evil:
And the LORD God commanded the man, saying, “Of every tree of the garden you may freely eat; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die. (Genesis 2:16-17 NKJV)
The second account makes the point there is only one way for death to enter the world: from a tree. By His work in creation, Jesus ensured that a tree would be the one and only way man could bring death into the world. Then He applied that same work by using a tree to bring life eternal into the world. His work of creation in the second account is specific in terms of name, day, 3-day period, and trees and how all of these inter-connect with the creation of the first man and woman. There is a single Author and a single Redeemer.
Trees also ensure the significance of a 3-day period in the first account since they were created on the third day and used on the sixth day. Since the garden was planted, those seeds were created on the third day. For an all knowing God, the tree of life, the tree of the knowledge of good and evil, and the tree which would form the cross were all created and chosen on the third day.
Also, there are two other records of the creation to consider:
This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him; Male and female created he them; and blessed them, and called their name Adam, in the day when they were created. (Genesis 5:1-2 KJV)
For in six days the LORD (YHVH) made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the LORD (YHVH) blessed the sabbath day, and hallowed it. (Exodus 20:11 KJV)
It is YHVH alone (not with Elohim) in Exodus who creates everything and blesses the seventh day. The way to reconcile all accounts is not by invoking different human sources. It is in the triune nature of God (Elohim) who creates all things through Jesus (YHVH).