Some trinitarians give Hosea 1:7 as an alleged example of two persons who are both called "Yahweh," and thus they offer Hosea 1:7 as an alleged proof of their doctrine of the trinity.
Here Yahweh is is contrasting the House of Judah with the House of Israel. In Hosea 1:6 he says that he will no longer have mercy on the house of Israel. To the house of Israel, Yahweh was, in effect, saying, "You are not my people, and I will not be your [God]." (Hosea 1:9) To the house of Judah, however, Yahweh is saying, "I will have mercy on the house of Judah, and will save them by Yahweh their God." Yahweh spoke of Himself by name as their God to emphasize that He, Yahweh, was still the God of house of Judah, and also that it would He, Yahweh, their God, who would deliver Judah, and that their deliverance would not be due to the implements that men use to conquer by means of battle. The JFB Commentary states regarding this:
more emphatic than "by Myself"; by that Jehovah (Me) whom they worship as their God, whereas ye despise Him.
Fausset, A. R., A.M. "Commentary on Hosea 1". "Commentary Critical and Explanatory on the Whole Bible".
Thus, while the house of Israel, as a whole, had come to despise Yahweh, Yahweh was emphasizing that He was still the God of the house of Judah.
What the trinitarian, however, would like for us to do regarding this verse, is (1) assume that the trinity dogma is true; (2) assume that "Yahweh" who is speaking is one person of Yahweh; (3) assume that when Yahweh said "by Yahweh" that this "Yahweh" is another person of Yahweh, who is not the first assumed person of Yahweh who speaking; and (4) then assume that these two assume persons who they claim are both called "Yahweh" are two persons of their alleged triune Yahweh. In reality, there is no need to add and read all these assumptions into the scripture.