Even if, α. He has no need of them, being most distinct of Himself: that is, God, since He is an altogether Singular Being, and distinct in His nature from all other things, does not need a distinguishing name: neither is a name, whether appellative, which belongs to distinctive species of the same genus, or proper, which distinguishes individuals of the same species, properly applied to God.
β. There are no such names that might fully and clearly express His most perfect Nature, according to Genesis 32:29; Judges 13:18; Proverbs 30:4, upon which passage consult WESSELIUS’ Nestorianismum et Adoptianismum redivivum confutatum, chapter XXII, § 261. Hence with good reason God is said to be Ineffable, no less than Incomprehensible, which we shall prove in § 11, which two things go together: for what the intellect is not able to grasp the tongue is not able to express; what is Incomprehensible in the language of the mind is Ineffable in the language of the mouth. Of course, God is Ineffable, not because nothing at all is allowed to be said concerning Him; but to the extent that it is not given to contrive any such apparatus of speech that might express what is fitting and sufficient for fully expressing the infinite Perfections of God, and the fullest signification of which the matter signified is not infinitely fuller.
Thus in a certain sense God is able to be called ἀνώνυμος/ nameless, as He is said to be by Trismegistus,[1] according to LACTANTIUS, Divinis Institutionibus, book I, chapter VI, “Mercury Trismegistus, lest anyone should ask the name of the highest and singular God, said that He is ἀνώνυμον/nameless; because He does not need the propriety of a name, namely, on account of His unity. These are his words: ὁ δὲ θεὸς, εἷς, ὁ δὲ εἷς ὀνόματος οὐ προσδέεται· ἔστι γὰρ ὁ ὢν ἀνώνυμος, God is one, but the one does not require a name: for the Being is nameless. Therefore, God does not have a name, because He is singular:” add LACTANTIUS’ libro de Ira Dei, chapter XI. Thus according to GREGORY NAZIANZEN, Oratione XXXVI, opera, tome I, page 589, τὸ θεῖον, ἀκατονόμαστον, the Deity is nameless. GREGORY NYSSEN, de eo quod non sint tres Dii, opera, tome 3, page 24, discoursing περὶ τῆς θείας φύσεως, concerning the divine nature, has among other things, Οὐκοῦν τὸ ἑκτὸς ὅρου, οὐδὲ ὀνόματι πάντως ὁρίζεται· —ὑπὲρ πᾶν ὄνομά φαμεν εἶναι τὸ θεῖον, and so that which is without limit is not limited by name…. We say that Deity is above all name. Similarly EUSEBIUS in his Demonstratione Euangelica, book IV, chapter I, page 144, describing God as One, says that He is πάσης κρείττονα προσηγορίας, ἄῤῥητον, ἀνέκφραστον, beyond all name, ineffable, inexpressible. And also RUFFINUS, in Symbolum, opera Hieronymi, tome 4, page 103, said among other things that God is ineffable substance. Attalus the martyr,[2] in EUSEBIUS’ Historia Ecclesiastica, book V, chapter I, page 163, ἐπερωτώμενος τί ὄνομα ἔχει ὁ Θεὸς, ἀπεκρίθη ὁ Θεὸς ὄνομα οὐκ ἔχει ὡς ἄνθρωπος, being asked what name God has, he answered that God does not have a name like a man.
[1] The Corpus Hermeticum is a collection of second century Greco-Egyptian wisdom texts, attributed to Hermes Trismegistus, or “Thrice-great”, a combination of the Greek Hermes and the Egyptian Thoth. Hermes was a messenger, one bringing knowledge and wisdom.
[2] Attalus was martyred for the testimony of Jesus near the Rhone River circa 172.