I don't think you understand the symbols behind names in the OT I guess.
Jesus was never ever referred to as Immanuel. No one ever called him that. The only time he was called Immanuel was when supposedly the angel told Mary that she will call him that.
Secondly, you talked about speaking to the house of david. It's true Ahaz refused to test God but as you can read God refused to let his nation be destroyed. Therefore the sign that was promised is that this son will be born to prove that GOS IS WITH US.
As we discussed the notion of that it is a dual prophecy is false. So we are left with the only choice of believing that She is a maid not a virgin. Now, since the kid was promised, right at the beginning of chapter 8 ISIAIH like in the case of Shearjashub names his son with a prophetic significance. The name warns of imminent destruction (the name means literally, “to speed the spoil, he hasteneth the prey”) and it has reference to the imminent destruction of Syria.
Now since we know it can't be a dual prophecy, and since the son was promised to the house of ISrael, and king Ahaz was there to hear the SIGN that will be shown to prove that God Is with HIS people as the name indicates, it's logical to assume that they are the same kid.
When Isiaih spoke to the house of david, Ahaz was part of the house of David, he was surounded by the house of David.
I'll quote myself,
Additional evidence that the prophet in Isaiah referred to an event soon to be realized, and not an event in Bethlehem eight hundred years later, may be found in the very next chapter in Isaiah , where a child called "Immanuel" is born. As proof that the boys in these two Isaiah chapters are one and the same. Both chapters mention the conquest of the lands of two kings "before the boy" reaches a certain age; this key phrase links the two chapters to the same child, Immanuel. The unborn and born child in the two Isaiah chapters are further linked by the appearance of the name Immanuel in both places. Immanuel, which in Hebrew means "God is with us" is a name which one may be sure was carefully chosen by the prophet to reassure the king that God would be on his side. Thus, in the second chapter we see the exclamation, "O Immanuel", which is Isaiah's proud announcement that the child was born and represented a sign that "God is with us".
Before Birth of Immanuel
Isaiah 7:14-16 " The young woman has conceived and will give birth to a son and will call him Immanuel. Before the boy knows enough to reject the wrong and choose the right, the land of the two kings you dread will be laid waste"
After Birth of Immanuel
Isaiah 8:3-8 " And she conceived and gave birth to a son. Before the boy knows how to say My father or My mother, the wealth of Damascus and the plunder of Samaria will be carried off ......O Immanuel"