Exodus 20, "And God spoke all these words:"

Background
The "Law" began by God peaking directly to everyone who was present at Mt Sinai:

¹ And God spoke all these words, saying...¹⁸ Now when all the people saw the thunder and the flashes of lightning and the sound of the trumpet and the mountain smoking, the people were afraid^[d] and trembled, and they stood far off ¹⁹ and said to Moses, “You speak to us, and we will listen; but do not let God speak to us, lest we die.” ²⁰ Moses said to the people, “Do not fear, for God has come to test you, that the fear of him may be before you, that you may not sin.” ²¹ The people stood far off, while Moses drew near to the thick darkness where God was. (Exodus 20) [ESV]

d. Samaritan, Septuagint, Syriac, Vulgate; Masoretic Text the people saw

At the request of the people, the "Law" from God was given by two methods:

• The Ten Commandments spoken by God to everyone (and written by God)
• All other laws spoken by God to Moses who wrote them down and told them to the people

The second method was not done "all at once" but over a period of time. At intervals we are told Moses told the people what God had said and that he wrote it down. For example:

Moses came and told the people all the words of the LORD and all the rules. And all the people answered with one voice and said, “All the words that the Lord has spoken we will do.” And Moses wrote down all the words of the LORD. (Exodus 24:3-4)

In the giving of the Ten Commandments, there is one, the command to observe the Sabbath, in which a reason for the command is given:

⁸ “Remember the Sabbath day, to keep it holy. ⁹ Six days you shall labor, and do all your work, ¹⁰ but the seventh day is a Sabbath to the LORD your God. On it you shall not do any work, you, or your son, or your daughter, your male servant, or your female servant, or your livestock, or the sojourner who is within your gates. ¹¹ For in six days the LORD made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the LORD blessed the Sabbath day and made it holy. (Exodus 20)

Since it is God who is speaking, the question is why wasn't the explanation for the Sabbath given in the first person as was the first command:

“I am the LORD your God, who brought you out of the land of Egypt, out of the house of slavery. “You shall have no other gods before me. (20:2-3)

For in six days the LORD [I] made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the LORD [I] blessed the Sabbath day and made it holy.

The Nature of God
The answer is found in the nature of God:

And God spoke all these words, saying...(20:1)

In the beginning, God created the heavens and the earth. (Genesis 1:1)

"God" is the Hebrew אֱלהִים which linguistically is plural:

Then God said, “Let us make man in our image... (Genesis 1:26)

First, if the Sabbath command had been given in the first person, one would expect it would be the first person plural, as in the making of man. However, that would seriously undermine the monotheistic message of a singular God:

For in six days we made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore we blessed the Sabbath day and made it holy.

Second, while God is plural and the discussion to make man was given in the plural (let us make...), the actual work of creation was done through Jesus:

All things were made through him, and without him was not any thing made that was made. (John 1:3)

Therefore, when "God" is speaking at Mt Sinai, the reason the explanation for the Sabbath is given as "the LORD" is to preserve the monotheistic nature of the triune God while stating the actual work was done by Jesus:

For in six days the LORD (Jesus) made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the LORD (Jesus) blessed the Sabbath day and made it holy.