The second century Church father and apologist Justin Martyr believed that the Father of the Lord Jesus had no name since he is beyond names. For Justin, to have a name meant that there would have to be someone greater or higher in authority that gave that specific individual his/her name. And since there is no higher authority than the Father, for Justin this indicated that the Father transcends all names.
Just further argued that since the Son was begotten of the Father, though not created, then he could be named. This is why Justin argued that names such as Jehovah, God, Captain, Word, Wisdom, Angel/Messenger belonged to the Son since it was the Son, not the Father, who appeared in the Old Testament as Jehovah God Almighty.
As one author explains:
Justin on God
Justin is of the opinion that because God is without origin, He is therefore nameless, because anyone who has a name has been given it by some elder. The words we use for God, like “Father and God and Creator and Master,” are not names in the strict sense, “but appellations derived from his good deeds and functions.” Even the word God is not a name, but “an opinion implanted in the nature of men of a thing that can hardly be explained.” Justin’s preferred “name” for God, at any rate, is Father, because it accurately reflects His having created all things.
For Justin, God the Father’s transcendence of the created world is such that a mediator is necessary by which He communicates with it. This is the Logos, the Son of God, who is the sole means by which God manifests Himself to human beings.
There are hints of the subordinationist error in Justin’s account of the relation between the Father and the Logos. It seems that for him, the Logos was originally a power in God and only was generated as a separate divine Person in order to create the world and subsequently manifest Himself in it. Justin insists that all the appearances of God in the Old Testament (under the form of an angel, or in the burning bush, for example) were of the Son, not the Father. It is almost as though the Father is “too transcendent” to be capable of manifesting Himself in a visible form, while the Logos is able to do so because He is “not as transcendent” as the Father. (Church Fathers: St. Justin Martyr, By Thomas V. Mirus, Mar 31, 2015 https://www.catholicculture.org/commentary/church-fathers-st-justin-martyr/; bold emphasis mine)
And in the words of Justin himself:
Chapter 10. How God is to be served
But we have received by tradition that God does not need the material offerings which men can give, seeing, indeed, that He Himself is the provider of all things. And we have been taught, and are convinced, and do believe, that He accepts those only who imitate the excellences which reside in Him, temperance, and justice, and philanthropy, and as many virtues as are peculiar to a God who is called by no proper name. And we have been taught that He in the beginning did of His goodness, for man’s sake, create all things out of unformed matter; and if men by their works show themselves worthy of this His design, they are deemed worthy, and so we have received — of reigning in company with Him, being delivered from corruption and suffering. For as in the beginning He created us when we were not, so do we consider that, in like manner, those who choose what is pleasing to Him are, on account of their choice, deemed worthy of incorruption and of fellowship with Him. For the coming into being at first was not in our own power; and in order that we may follow those things which please Him, choosing them by means of the rational faculties He has Himself endowed us with, He both persuades us and leads us to faith. And we think it for the advantage of all men that they are not restrained from learning these things, but are even urged thereto. For the restraint which human laws could not effect, the Word, inasmuch as He is divine, would have effected, had not the wicked demons, taking as their ally the lust of wickedness which is in every man, and which draws variously to all manner of vice, scattered many false and profane accusations, none of which attach to us…
Chapter 63. How God appeared to Moses
And all the Jews even now teach that the NAMELESS God spoke to Moses; whence the Spirit of prophecy, accusing them by Isaiah the prophet mentioned above, said The ox knows his owner, and the ass his master’s crib; but Israel does not know Me, and My people do not understand. Isaiah 1:3 And Jesus the Christ, because the Jews knew not what the Father was, and what the Son, in like manner accused them; and Himself said, No one knows the Father, but the Son; nor the Son, but the Father, and they to whom the Son reveals Him. Matthew 11:27 Now the Word of God is His Son, as we have before said. And He is called Angel and Apostle; for He declares whatever we ought to know, and is sent forth to declare whatever is revealed; as our Lord Himself says, He that hears Me, hears Him that sent Me. Luke 10:16 From the writings of Moses also this will be manifest; for thus it is written in them, And the Angel of God spoke to Moses, in a flame of fire out of the bush, and said, I am that I am, the God of Abraham, the God of Isaac, the God of Jacob, the God of your fathers; go down into Egypt, and bring forth My people. Exodus 3:6 And if you wish to learn what follows, you can do so from the same writings; for it is impossible to relate the whole here. But so much is written for the sake of proving that Jesus the Christ is the Son of God and His Apostle, being of old the Word, and appearing sometimes in the form of fire, and sometimes in the likeness of angels; but now, by the will of God, having become man for the human race, He endured all the sufferings which the devils instigated the senseless Jews to inflict upon Him; who, though they have it expressly affirmed in the writings of Moses, And the angel of God spoke to Moses in a flame of fire in a bush, and said, I am that I am, the God of Abraham, and the God of Isaac, and the God of Jacob, yet maintain that He who said this was the Father and Creator of the universe. Whence also the Spirit of prophecy rebukes them, and says, Israel does not know Me, my people have not understood Me. Isaiah 1:3 And again, Jesus, as we have already shown, while He was with them, said, No one knows the Father, but the Son; nor the Son but the Father, and those to whom the Son will reveal Him. Matthew 11:27 The Jews, accordingly, being throughout of opinion that it was the Father of the universe who spoke to Moses, THOUGH HE WHO SPOKE 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. And of old He appeared in the shape of fire and in the likeness of an angel to Moses and to the other prophets; but now in the times of your reign, having, as we before said, become Man by a virgin, according to the counsel of the Father, for the salvation of those who believe in Him, He endured both to be set at nought and to suffer, that by dying and rising again He might conquer death. And that which was said out of the bush to Moses, I am that I am, the God of Abraham, and the God of Isaac, and the God of Jacob, and the God of your fathers, Exodus 3:6 this signified that they, even though dead, are yet in existence, and are men belonging to Christ Himself. For they were the first of all men to busy themselves in the search after God; Abraham being the father of Isaac, and Isaac of Jacob, as Moses wrote. (First Apology; bold and capital emphasis mine)
Chapter 6. Names of God and of Christ, their meaning and power
But to the Father of all, who is unbegotten there is no name given. For by whatever name He be called, He has as His elder the person who gives Him the name. But these words Father, and God, and Creator, and Lord, and Master, are not names, but appellations derived from His good deeds and functions. And His Son, who alone is properly called Son, the Word who also was with Him and was begotten before the works, when at first He created and arranged all things by Him, is called Christ, in reference to His being anointed and God’s ordering all things through Him; this name itself also containing an unknown significance; as also the appellation God is not a name, but an opinion implanted in the nature of men of a thing that can hardly be explained. But Jesus, His name as man and Saviour, has also significance. For He was made man also, as we before said, having been conceived according to the will of God the Father, for the sake of believing men, and for the destruction of the demons. And now you can learn this from what is under your own observation. For numberless demoniacs throughout the whole world, and in your city, many of our Christian men exorcising them in the name of Jesus Christ, who was crucified under Pontius Pilate, have healed and do heal, rendering helpless and driving the possessing devils out of the men, though they could not be cured by all the other exorcists, and those who used incantations and drugs. (Second Apology; bold and capital emphasis mine)
Finally:
Chapter 21. The namelessness of God
For God cannot be called by any proper name, for names are given to mark out and distinguish their subject-matters, because these are many and diverse; but neither did any one exist before God who could give Him a name, nor did He Himself think it right to name Himself, seeing that He is one and unique, as He Himself also by His own prophets testifies, when He says, I God am the first, and after this, And beside me there is no other God. Isaiah 44:6 On this account, then, as I before said, God did not, when He sent Moses to the Hebrews, mention any name, but by a participle He mystically teaches them that He is the one and only God. For, says He; I am the Being; manifestly contrasting Himself, the Being, with those who are not, that those who had hitherto been deceived might see that they were attaching themselves, not to beings, but to those who had no being. Since, therefore, God knew that the first men remembered the old delusion of their forefathers, whereby the misanthropic demon contrived to deceive them when he said to them, If you obey me in transgressing the commandment of God, you shall be as gods, calling those gods which had no being, in order that men, supposing that there were other gods in existence, might believe that they themselves could become gods. On this account He said to Moses, I am the Being, that by the participle being He might teach the difference between God who is and those who are not. Men, therefore, having been duped by the deceiving demon, and having dared to disobey God, were cast out of Paradise, remembering the name of gods, but no longer being taught by God that there are no other gods. For it was not just that they who did not keep the first commandment, which it was easy to keep, should any longer be taught, but should rather be driven to just punishment. Being therefore banished from Paradise, and thinking that they were expelled on account of their disobedience only, not knowing that it was also because they had believed in the existence of gods which did not exist, they gave the name of gods even to the men who were afterwards born of themselves. This first false fancy, therefore, concerning gods, had its origin with the father of lies. God, therefore, knowing that the false opinion about the plurality of gods was burdening the soul of man like some disease, and wishing to remove and eradicate it, appeared first to Moses, and said to him, I am He who is. For it was necessary, I think, that he who was to be the ruler and leader of the Hebrew people should first of all know the living God. Wherefore, having appeared to him first, as it was possible for God to appear to a man, He said to him, I am He who is; then, being about to send him to the Hebrews, He further orders him to say, He who is has sent me to you. (Hortatory Address to the Greeks; bold emphasis mine
Hence, for Justin the Father is not Jehovah even though he believed that the Father is the timeless, uncreated God who transcends all creation. Rather, it is Jesus whose name is Jehovah and is therefore that very God who appears throughout the Old Testament under very names and guises.
And since the Hebrew Bible affirms that Jehovah is beginningless, almighty and supreme over all creation as the Most High,
“See now that I, even I, am he, And there is no god with me: I kill, and I make alive; I wound, and I heal; And there is none that can deliver out of my hand.” Deuteronomy 32:39 American Standard Version (ASV)
“I will give thanks unto Jehovah according to his righteousness, And will sing praise to the name of Jehovah Most High.” Psalm 7:17 ASV
“The earth is Jehovah’s, and the fulness thereof; The world, and they that dwell therein. For he hath founded it upon the seas, And established it upon the floods… Lift up your heads, O ye gates; And be ye lifted up, ye everlasting doors: And the King of glory will come in. Who is the King of glory? Jehovah strong and mighty, Jehovah mighty in battle. Lift up your heads, O ye gates; Yea, lift them up, ye everlasting doors: And the King of glory will come in. Who is this King of glory? Jehovah of hosts, He is the King of glory.” Psalm 24:1-2, 7-10 ASV
“That they may know that thou alone, whose name is Jehovah, Art the Most High over all the earth.” Read full chapter Psalm 83:18 ASV
“Book IV A Prayer of Moses the man of God. Lord, thou hast been our dwelling-place In all generations. Before the mountains were brought forth, Or ever thou hadst formed the earth and the world, Even from everlasting to everlasting, thou art God.” Psalm 90:1-2 ASV
“Jehovah reigneth; he is clothed with majesty; Jehovah is clothed with strength; he hath girded himself therewith: The world also is established, that it cannot be moved. Thy throne is established of old: Thou art from everlasting.” Psalm 93:1-2 ASV
“For thou, Jehovah, art most high above all the earth: Thou art exalted far above all gods.” Psalm 97:9 ASV
This means that Jesus, according to Justin, is none other than God Almighty Most High who became human!
FURTHER READING
Justin Martyr’s Witness to Christ’s essential and eternal Deity
Revisiting Shabir Ally’s Distortion of Justin Martyr Pt. 1
Revisiting Shabir Ally’s Distortion of Justin Martyr Pt. 2
THE EARLY CHURCH ON THE ETERNAL BEGETTING OF THE SON
CHURCH FATHERS ON ETERNAL GENERATION
Answering Islam Blog 
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