I AM is not a proper name

For having heard in Egypt that God had said to Moses, when He was about to send him to the Hebrews, “I am that I am,” he understood that God had not mentioned to him His own proper name.

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.” 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.

Justin Martyr
Hortatory Address to the Greeks
Chapter XX & XXI

The Father has no name. The Son is begotten.

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;

Justin Martyr
Second Apology
Chapter VI

Christ is the God of Abraham, Isaac and Jacob

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,” this signified that they, even though dead, are yet in existence, and are men belonging to Christ Himself.

Justin Martyr
First Apology
Chapter LXIII

Christ spoke to Moses in the burning bush

For at that juncture, when Moses was ordered to go down into Egypt and lead out the people of the Israelites who were there, and while he was tending the flocks of his maternal uncle in the land of Arabia, our Christ conversed with him under the appearance of fire from a bush, and said, “Put off thy shoes, and draw near and hear.” And he, when he had put off his shoes and drawn near, heard that he was to go down into Egypt and lead out the people of the Israelites there; and he received mighty power from Christ, who spoke to him in the appearance of fire, and went down and led out the people, having done great and marvelous things; which, if you desire to know, you will learn them accurately from his writings.

Justin Martyr
First Apology
Chapter LXII

God created matter and has no personal name

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.

Justin Martyr
First Apology
Chapter X