And no matter what form He takes, He is still God. The title is given to those three because those three are the one and same God.
Yes, they are the same God (Deity, not being), there is only one God. And you have agreed that they are three beings correct? That is what I have been saying. There is the Father, the Son and the holy Spirit. The Father is not the Son, the Son is not the Holy Spirit, yet all three are deity.
I think what you are missing is that John uses the word God in two different senses in John 1. that that is why keep asking people to define "God". In the Scriptures the word "God" is used in different senses. For instance, it is use as name for the Father, it is also used to say that one is divine. these are the two senses that John uses, the first time he is using it as a name for the Father, the second time he is using it to say that the word is divine.
We can see this with the example of the Hebrew word translated Adam. it is used as a name for the first man, the word however also means, mankind. So, we could say that Eve was with Adam and Eve was Adam. In this statement we are not saying that Eve is the same person as Adam we are saying that Eve was with Adam, the first man and Eve was Adam, she was human or mankind. This is the way that John uses the word God.
The Early Church Fathers: Ante-Nicene Fathers Volume 1
Justin Martyr 160 AD
And again, Jesus, as we have already shown, while He was with them, said, “No one knoweth the Father, but the Son; nor the Son but the Father, and those to whom the Son will reveal Him.” (Matt. 11:27) The Jews, accordingly, being throughout of opinion that it was the Father of the universe who spake to Moses, though He who spake to him was indeed the Son of God, who is called both Angel and Apostle, are justly charged, both by the Spirit of prophecy and by Christ Himself, with knowing neither the Father nor the Son.
For they who affirm that the Son is the Father, are proved neither to have become acquainted with the Father, nor to know that the Father of the universe has a Son; who also, being the first-begotten Word of God, is even God.
The Early Church Fathers: Ante-Nicene Fathers Volume 1
Hippolytus 205 AD
The Early Church Fathers: Ante-Nicene Fathers Volume 5
Against the Heresy of One Noetus..
Some others are secretly introducing another doctrine, who have become disciples of one Noetus, who was a native of Smyrna, (and) lived not very long ago. This person was greatly puffed up and inflated with pride, being inspired by the conceit of a strange spirit. He
alleged that Christ was the Father Himself, and that the Father Himself was born, and suffered, and died. Ye see what pride of heart and what a strange inflated spirit had insinuated themselves into him. From his other actions, then, the proof is already given us that he spoke not with a pure spirit; for he who
blasphemes against the Holy Ghost is cast out from the holy inheritance. He alleged that he was himself Moses, and that Aaron was his brother.
When the blessed presbyters heard this, they summoned him before the Church, and examined him. But he denied at first that he held such opinions. Afterwards, however, taking shelter among some, and having gathered round him some others who had embraced the same error, he wished thereafter to uphold his dogma openly as correct. And the blessed presbyters called him again before them, and examined him. But he stood out against them, saying, “What evil, then, am I doing in glorifying Christ?” And the presbyters replied to him, “We too know in truth one God; we know Christ; we know that the Son suffered even as He suffered, and died even as He died, and rose again on the third day, and is at the right hand of the Father, and cometh to judge the living and the dead. And these things which we have learned we allege.”
Then, after examining him, they expelled him from the Church. And he was carried to such a pitch of pride, that he established a school.
The Early Church Fathers: Ante-Nicene Fathers Volume 5
Novatian 235AD
Argument.—In Fine, Notwithstanding the Said Heretics Have Gathered the Origin of Their Error from Consideration of What Is Written:Although We Call Christ God, and the Father God, Still Scripture Does Not Set Forth Two Gods, Any More than Two Lords or Two Teachers.
And now, indeed, concerning the Father, and the Son, and the Holy Spirit, let it be sufficient to have briefly said thus much, and to have laid down these points concisely, without carrying them out in a lengthened argument. For they could be presented more diffusely and continued in a more expanded disputation, since the whole of the Old and New Testaments might be adduced in testimony that thus the true faith stands. But because heretics, ever struggling against the truth, are accustomed to prolong the controversy of pure tradition and Catholic faith, being offended against Christ; because He is, moreover, asserted to be God by the Scriptures also, and this is believed to be so by us;
we must rightly—that every heretical calumny may be removed from our faith—contend, concerning the fact that Christ is God also, in such a way as that it may not militate against the truth of Scripture; nor yet against our faith, how there is declared to be one God by the Scriptures, and how it is held and believed by us.
For as well they who say that Jesus Christ Himself is God the Father, as moreover they who would have Him to be only man,
have gathered thence the sources and reasons of their error and perversity; because when they perceived that it was written [Galatians 3:20; Deuteronomy 6:4] that “God is one,” they thought that they could not otherwise hold such an opinion than by supposing that it must be believed either that Christ was man only, or really God the Father. And they were accustomed in such a way to connect their sophistries as to endeavour to justify their own error. And thus they who say that Jesus Christ is the Father argue as follows:—If God is one, and Christ is God, Christ is the Father, since God is one. If Christ be not the Father, because Christ is God the Son, there appear to be two Gods introduced, contrary to the Scriptures. And they who contend that Christ is man only, conclude on the other hand thus:—If the Father is one, and the Son another, but the Father is God and Christ is God, then there is not one God, but two Gods are at once introduced, the Father and the Son; and if God is one, by consequence Christ must be a man, so that rightly the Father may be one God. Thus indeed the Lord is, as it were, crucified between two thieves, even as He was formerly placed; and thus from either side He receives the sacrilegious reproaches of such heretics as these.
The Early Church Fathers: Ante-Nicene Fathers Volume 3.
Tertullian 213AD
Chap. XXIX.—It Was Christ that Died, the Father Is Incapable of Suffering Either Solely or with Another. Blasphemous Conclusions Spring from Praxeas’ Premises.
Silence! Silence on such blasphemy. Let us be content with saving that Christ died, the Son of the Father; and let this suffice, because the Scriptures have told us so much. For even the apostle, to his declaration—which he makes not without feeling the weight of it—that “Christ died,” immediately adds, “according to the Scriptures,” (1 Corinthians 15:3) in order that he may alleviate the harshness of the statement by the authority of the Scriptures, and so remove offence from the reader. Now, although when two substances are alleged to be in Christ—namely, the divine and the human— 626 it plainly follows that the divine nature is immortal, and that which is human is mortal, it is manifest in what sense he declares “Christ died”—even in the sense in which He was flesh and Man and the Son of Man, not as being the Spirit and the Word and the Son of God. In short, since he says that it was Christ (that is, the Anointed One) that died, he shows us that that which died was the nature which was anointed; in a word, the flesh. Very well, say you; since we on our side affirm our doctrine in precisely the same terms which you use on your side respecting the Son, we are not guilty of blasphemy against the Lord God, for we do not maintain that He died after the divine nature, but only after the human.
Nay, but you do blaspheme;
because you allege not only that the Father died, but that He died the death of the cross. For “cursed are they which are hanged on a tree,” (Galatians 3:13)—a curse which, after the law,
is compatible to the Son (inasmuch as “Christ has been made a curse for us,” (Galatians 3:13)
but certainly not the Father); since,
however, you convert Christ into the Father, you are chargeable with blasphemy against the Father. But when we assert that Christ was crucified, we do not malign Him with a curse; we only re-affirm the curse pronounced by the law: (Deuteronomy 21:23) nor indeed did the apostle utter blasphemy when he said the same thing as we. (Galatians 3:13) Besides, as there is no blasphemy in predicating of the subject that which is fairly applicable to it; so, on the other hand, it is blasphemy when that is alleged concerning the subject which is unsuitable to it. On this principle, too, the Father was not associated in suffering with the Son. The heretics, indeed, fearing to incur direct blasphemy against the Father, hope to diminish it by this expedient: they grant us so far that the Father and the Son are Two; adding that, since it is the Son indeed who suffers, the Father is only His fellow-sufferer. But how absurd are they even in this conceit! For what is the meaning of “fellow-suffering,” but the endurance of suffering along with another? Now if the Father is incapable of suffering, He is incapable of suffering in company with another; otherwise, if He can suffer with another, He is of course capable of suffering. You, in fact, yield Him nothing by this subterfuge of your fears. You are afraid to say that He is capable of suffering whom you make to be capable of fellow-suffering. Then, again, the Father is as incapable of fellow-suffering as the Son even is of suffering under the conditions of His existence as God. Well, but how could the Son suffer, if the Father did not suffer with Him? My answer is, The Father is separate from the Son, though not from Him as God. For even if a river be soiled with mire and mud, although it flows from the fountain identical in nature with it, and is not separated from the fountain, yet the injury which affects the stream reaches not to the fountain; and although it is the water of the fountain which suffers down the stream, still, since it is not affected at the fountain, but only in the river, the fountain suffers nothing, but only the river which issues from the fountain. So likewise the Spirit of God, whatever suffering it might be capable of in the Son, yet, inasmuch as it could not suffer in the Father, the fountain of the Godhead, but only in the Son, it evidently could not have suffered, as the Father. But it is enough for me that the Spirit of God suffered nothing as the Spirit of God, since all that It suffered It suffered in the Son. It was quite another matter for the Father to suffer with the Son in the flesh. This likewise has been treated by us. Nor will any one deny this, since even we are ourselves unable to suffer for God, unless the Spirit of God be in us, who also utters by our instrumentality whatever pertains to our own conduct and suffering; not, however, that He Himself suffers in our suffering, only He bestows on us the power and capacity of suffering. Bookmark Name Bookmark Date Bookmark Text Edit commentary text here
This is just a few quotes, there are quite a bit more. This shows that the Early church fought vehemently "AGAINST" the doctrine that you are espousing. It was known as Monarchianism. They argued that the Father and the Son were "NOT" the same being.