I have some research on this and made some observations that might be helpful toward formulating an answer. IT was just too much to share in comments.
Hebrews often name their babies in praise to some attribute of God at work in their life. Thus, names contain El, or Yah.
Some seem to indicate relationship to God, like, Elichai, meaning my God alive.
Others do not indicate relationship, like Elead, meaning, God eternal.
Doubtless, neither Elead's mom nor anyone else thought that she was saying this baby was God eternal or we would have heard a lot more about it!
Similarly, the prophecy given by Isaiah earlier in chapter 7, that a young woman would conceive and bear a child and his name would be called Immanuel, meaning God with us does not mean the child was God with them. We know that God told Israel, when a prophet spoke, the way they would know if a thing were from God, or if a prophet spoke presumptuously, was if that thing came to pass (Deuteronomy 18:22). Isaiah is telling Israel they will be invaded and overtaken by the Assyrians; but, he also offers words of hope that a government will arise. The only way people would know if what he said was certainly from God, is if what he fortold came true. What comfort is hope if one is not certain it is true or from God. The only way that Israel would know if these words of hope were certain and true, was if something he spoke already transpired as he said. He prophecies that a child will be born, his name will be called Immanuel, and before he is old enough to discern between good and evil, the Assyrians will invade and remove them from their land. While, to my knowledge, we do not hear anything more about the child, Immanuel, we do know the Assyrians did indeed invade as foretold, and logically we assume the baby was born first as prophesied and all this happened before he was old enough to discer between good or evil. (IF it did not come true then Isaiah would not be regarded to this day as a prophet) Israel would have known from these events that also the promised hope would come just as surely. It is not illogical to assume that in that day, no one thought that baby Emmanuel was actually God with them. The child's name was only prophetic to assure Israel God was with them though things looked bleak and that the rest of the prophecy spoken of in chapter 9 would also occur, that a Governor would come.
So, it seems that we cannot always take a Hebrew name and say it says the child himself is those things the name says; sometimes the child's name serves as a memorial of Gods attributes and even promise, in the community.
Now, looking at this long name in chapter 9, Its elements are not logically congruous. One element is Almighty God and another is Prince of Peace. One cannot be Almighty and Prince simultaneously for a prince would be, by definition, subordinate to the Almighty. Could it be that this name, like the Hebrew name, Elichai, show a relationship between two people?
Observe now that one of the words, translated by some "comforter" is actually a verb. I am no Hebrew scholar, just relying on libronx ESV interlinear which shows "counselor" to be "verb, qal, active, pure noun participle, singular, masculine, normal." If I understand correctly, a noun participle acts like an adjective, in this case the verb is to advise/counsel. Could it be that this name shows the activity of God in relationship to the other.
It is not illogical that this prophecy speaks of a hope that there would be a Prince of Peace who would come in the wonderful counsel of Almighty God and Everlasting Father.
Isaac Leeser translates it accordingly:
Wonderful, counsellor of the mighty God, of the everlasting Father,
the prince of peace.*"