This shows you do not know the scripture showing where both persons talking have been identified as YHWH. This suggests you do not recognize how God has interacted with people on earth. You are right when you note there must be different persons speaking. This is what the Trinitarian notes when identifying two or more persons of the Godhead yet being singly as God. It does not have to match your experience as a human since this God is not made in man's image. It would help if you made an argument that actually spoke against the Trinitarian concepts.When two different persons speak to one another it means they aren't the same person. You act as if men, angels, and God can't be in the same location or vacinity at the same time. There is nothing that clearly states that the angel of the Lord is YHWH Himself. It's also nonsensical that the LORD would be His own messenger because being a messenger implies giving messages for someone else. Someone who is speaking on their own behalf is not a messenger.
Also, Jesus and the angel of the Lord are in the same context yet not the same person. So we can rule out Jesus being the angel of the Lord.
Matthew 28:2And, behold, there was a great earthquake: for the angel of the Lord descended from heaven, and came and rolled back the stone from the door, and sat upon it.Luke 22:43"And there appeared an angel unto him from heaven, strengthening him."
In summary you have noted:
* that a single person must have another person to have a chat so there must be multiple persons in the Godhead
* that the multiple persons of the Godhead is different from the human experience, which should not be a surprise
* that there are multiple persons involved in these instances that could mistakenly miss that this is multiple persons of the Godhead