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, “without ceasing to be the unseen Yahweh enthroned above, Yahweh is also free to assume a perceptible form, in which he ‘has objectivity for those to whom he is manifest.'” This objective form comes as Word, Spirit, Wisdom, and also in the name Yahweh, which is not “an external attribute of Yahweh, but the form in which the invisible Yahweh in heaven becomes present and manifest on earth. ‘The name of Yahweh is the form in which Yahweh comes to Israel, has dealings with it, is manifest to it.’ . . . Through the name, God chooses a people, makes it his own, and rules it.”
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.