God's great and incommunicable name Jehovah is always in the singular and is never used plurally; the reason of which is because it is expressive of his essence, which is but one. It is the same with "I AM that I AM." But the first name of God we meet with in Scripture, and that in the first verse of it, is plural; "In the beginning God (Elohim) created the heaven and the earth" (Gen. 1:1), and therefore must design more than one, at least two, and yet not precisely two, or two only; then it would have been dual. But it is plural, and cannot design fewer than three.
Now Moses might have made use of other names of God in his account of the creation; as his name Jehovah, by which he made himself known to Moses and to the people of Israel; or Eloah, the singular of Elohim, which is used by him (Deut. 32:15, 16) and in the book of Job frequently. So, it was not a lack of singular names of God, nor the barrenness of the Hebrew language, which obliged him to use a plural word. It was no doubt of choice and with design; and which will be more evident when it is observed that one end of the writings of Moses is to root out the polytheism of the heathens and to prevent the people of Israel from going into it. Therefore, it may seem strange that he should begin his history with a plural name of God. He must have some design in it, which could not be to inculcate a plurality of gods, for that would be directly contrary to what he had in view in writing and to what he asserts (Deut. 6:4).
And then the historian goes on to make mention of the Persons of the Trinity, who, besides the Father, included in this name, are the Spirit of God, that moved upon the face of the waters, and the Word of God (Gen. 1:2), which said, "Let there be light, and there was light"; and which spoke that, and all things, out of nothing; see (John 1:1-3). And it may be further observed, that this plural word Elohim is, in this passage, in construction with a singular verb, bara, rendered "created"; which some have thought is designed to point out a plurality of persons and the unity of the divine essence: but if this is not judged sufficient to build it upon, let it be further observed, that the word Elohim is sometimes in construction with a plural verb, as in Gen. 20:13; Gen. 35:7; 2 Sam. 7:23, where Elohim is said to cause Abraham to wander from his father's house; to appear to Jacob; and to go forth to redeem Israel - all which are personal actions.
Adapted from A Body of Doctrinal Divinity, Book 1, Chapter 27, by John Gill.