Kendal Soulen (The Divine Names and the Holy Trinity, 97) summarizes Barth’s treatment of the implicit Trinitarianism of the Old Testament:
“the Old testament testifies to Yahweh in three distinct ways. ‘Yahweh’ refers ‘a first time’ to the unseen God who is invisibly enthroned over all things, who remains forever hidden even in the act of revelation itself. It also refers again ‘in another way’ to God insofar as he is truly known by this or that person, as revelation reaches its goal in human recognition and acknowledgement. These strands of biblical testimony correspond to the first and last elements of the sentence ‘God reveals himself as Lord,’ to God the Actor and God the Result. Barth’s main interest, however, is not with these, but with the third strand of testimony, which concerns God’s ability to be God ‘the Object,’ to reveal ‘Himself as Lord.'”
Thus, Israel constructs a house not for Yahweh but for the Name. Communion with the name is communion with Yahweh. As Barth puts it, “To have knowledge of the name of Yahweh, and to that degree knowledge of Yahweh himself, and to participate in His revelation, is to be a partner in the covenant made by Him.'”
Thus Jesus comes saying “I am,” identifying Himself with Yahweh, while at the same time speaking of a Father in heaven, to whom He will return and with whom He will be enthroned.