Objection 1. It seems that this name, "God," is not a name of the nature. For Damascene says (De Fide Orth. 1) that "God Theos is so called from the theein [which means to care of] and to cherish all things; or from the aithein, that is to burn, for our God is a fire consuming all malice; or from theasthai, which means to consider all things." But all these names belong to operation. Therefore this name "God" signifies His operation and not His nature.
Objection 2. Further, a thing is named by us as we know it. But the divine nature is unknown to us. Therefore this name "God" does not signify the divine nature.
On the contrary, Ambrose says (De Fide i) that "God" is a name of the nature.
I answer that, Whence a name is imposed, and what the name signifies are not always the same thing. For as we know substance from its properties and operations, so we name substance sometimes for its operation, or its property; e.g. we name the substance of a stone from its act, as for instance that it hurts the foot [loedit pedem]; but still this name is not meant to signify the particular action, but the stone's substance. The things, on the other hand, known to us in themselves, such as heat, cold, whiteness and the like, are not named from other things. Hence as regards such things the meaning of the name and its source are the same.
Because therefore God is not known to us in His nature, but is made known to us from His operations or effects, we name Him from these, as said in 1; hence this name "God" is a name of operation so far as relates to the source of its meaning. For this name is imposed from His universal providence over all things; since all who speak of God intend to name God as exercising providence over all; hence Dionysius says (Div. Nom. ii), "The Deity watches over all with perfect providence and goodness." But taken from this operation, this name "God" is imposed to signify the divine nature.
Reply to Objection 1. All that Damascene says refers to providence; which is the source of the signification of the name "God."
Reply to Objection 2. We can name a thing according to the knowledge we have of its nature from its properties and effects. Hence because we can know what stone is in itself from its property, this name "stone" signifies the nature of the stone itself; for it signifies the definition of stone, by which we know what it is, for the idea which the name signifies is the definition, as is said in Metaph. iv. Now from the divine effects we cannot know the divine nature in itself, so as to know what it is; but only by way of eminence, and by way of causality, and of negation as stated above (Question 12, Article 12). Thus the name "God" signifies the divine nature, for this name was imposed to signify something existing above all things, the principle of all things and removed from all things; for those who name God intend to signify all this.
Source: Summa Theologica (New Advent)