We pray in Jesus’s name because he is the reason that we have access to the Most High God. Without the atonement, we would be irreconcilably impure and therefore excluded from God’s presence, for “there cannot any unclean thing enter into the kingdom of God” (1 Ne. 15:34). Only through the atonement can our impurity be cleansed; and therefore, only through Jesus’s name, as the representation of his atonement, may we approach God in prayer.
In this case, as the twelve and the multitude pray to Jesus, he redirects their prayers to the Father by saying, “I pray unto thee for them.” The only one able to answer their prayers is the Father. Jesus therefore prays for them directly, literally becoming the Mediator whose atonement enables all of our prayers.
Reference: The prayer that the people offer—one that Jesus opens to all who accept the gospel—is to “be in them as thou, Father, art in me, that we may be one.” This language echoes Jesus’s teaching in the New Testament:
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. (John 17:20–22)
As in the Old World, so in the New. Jesus prays that those who believe will become one with the Father, as Jesus is. What is this “oneness?” It clearly means not corporeal unity, but conceptual unity. While there may be diverse people, we can all be of “one heart” (1 Chr. 12:38, 2 Chr. 30:12, Jer. 32:39, Ezek. 11:19, Acts 4:32, 2 Ne. 1:21).