The ordinance of baptism is to be done in the names of all three members of the Godhead. And, correspondingly, Christ wants us to understand the unity that exists between these three. They are "one" with each other.
The "oneness" of God the Father, His Son, and the Holy Ghost was discussed by Christ in His teachings of the New Testament. The Intercessory Prayer recorded in John 17, includes His expansion on the idea. There Christ taught: "Neither pray I for these alone, but for them also which shall believe on me through their word; That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me. And the glory which thou gavest me I have given them; that they may be one, even as we are one: I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me. Father, I will that they also, whom thou hast given me, be with me where I am; that they may behold my glory, which thou hast given me: for thou lovedst me before the foundation of the world." (John 17: 20-24.)
This unity between the Father, Son and Holy Ghost is a point of doctrine raised by Christ in this teaching. It is important for us to understand that the message we receive from the Holy Ghost will be the same as the message we would receive from Christ. It is also important for us to rely on and have faith in Christ and the Holy Ghost so that we may trust them to bring us to the Father.
It is also a model for us to follow. We are supposed to drop our fears and worries, shed our ambitions and desires, and come together in unity until we are "one." The non-competitive, fully cooperative manner the Father, Son and Holy Ghost are "one" is the model of Zion itself. Divisions and strifes are unthinkable between the members of the Godhead. In contrast, among us they are unavoidable.
The ideal is always the standard. We push toward perfection. The Father lives in absolutes. Therefore we strive for the absolute, all the while struggling with our relative and incremental improvement. We are in the process of being "added upon." (Abr. 3: 26.) The Father, on the other hand, dwells where there is nothing but perfection. (D&C 1: 31.) So for us the Mediator and the Savior establish the bridge between where we are forbidden to enter in sin, and the borrowed cleanliness which momentarily lets us enter in.
We are to become "one" with Them. It is a distant goal, to be accomplished after being "added upon" for a long time. Joseph taught in the King Follett Discourse: "Here, then, is eternal life—to know the only wise and true God; and you have got to learn how to be gods yourselves, and to be kings and priests to God, the same as all gods have done before you, namely, by going from one small degree to another, and from a small capacity to a great one; from grace to grace, from exaltation to exaltation, until you attain to the resurrection of the dead, and are able to dwell in everlasting burnings, and to sit in glory, as do those who sit enthroned in everlasting power... When you climb up a ladder, you must begin at the bottom, and ascend step by step, until you arrive at the top; and so it is with the principles of the gospel—you must begin with the first, and go on until you learn all the principles of exaltation. But it will be a great while after you have passed through the veil before you will have learned them. It is not all to be comprehended in this world; it will be a great work to learn our salvation and exaltation even beyond the grave."
To become "one" will be to reach the end of a long journey. We can have promises of that end. We can receive covenants that will bring us there. But our arrival will "be a great while after [we] have passed through the veil" for "it is not all to be comprehended in this world." Moses was told that, also. (Moses 1: 5.) We may be initiated, but to enter in will be "a great work to learn our salvation and exaltation even beyond the grave."
So the ideal of "one" with the Father, Son and Holy Ghost for us is distant, to be sought, to be kept before us, but not to be obtained until some time later. But to be "one" with each other is another matter. Being "one" is required of us for Zion to return. Zion is required for the Lord to dwell among us again. He is going to return to a Zion, no matter how few may be involved. He will come even if only two or three gather in His name. (Matt. 18: 20.) Zion may be small, but it will nonetheless be Zion before He can visit with her.