Isa 44:6 Thus saith Yahweh the King of Israel, and his redeemer Yahweh of hosts; I am the first, and I am the last; and beside me there is no Elohim.
This is the reason why I am trying to figure out who Yahweh is. From my understanding of the Trinity, for the Trinity to agree with the above verse The Father must be Yahweh, The Son must be Yahweh, and The Holy Spirit must also be Yahweh since beside Yahweh there is no Elohim.
This is why I would like to determine whether Yahweh is a name or a title. If it is a title it can be applied to three persons just as Elohim can be applied to three persons. But if Yahweh is a name, can three persons share the same personal name?