Part of the problem here is that in the West a lot of theology before a certain point in time was in Latin, and you do find discussions of divine simplicity in terms of identitas, deriving from the word idem. Unfortunately, our term 'identity' is not usually a good translation of identitas, despite the fact that it's easy to read the latter as the former. Identitas just means 'sameness', and it can apply to any kind of sameness. The most common meaning of identitas, in fact, is 'sameness in kind', although it can also mean other kinds of things.
Part of the problem, however, is how history is read. And Augustine, who is often accused of arguing for this "absolute divine simplicity" is a good example. The accusation is simply incorrect. Most of the passages in question are simply being misread and often don't have anything directly to do with simplicity. And when we actually look at Augustine's doctrine of simplicity we find (1) that it's a pretty spare account that can be read more than one way; and (2) that Augustine nonetheless characterizes divine simplicity in a way that is very difficult to reconcile with the notion that he accepts "absolute divine simplicity".
Augustine says very, very little about divine simplicity in his writings. It gets mentioned, usually in passing without much comment, but even the mentions are fairly scattered. In De Trinitate, for instance, which people often point to as their source, most of the mentions just tell us that Father, Son, and Holy Spirit are equal because God is simple; God cannot be changeable because God is simple; divine simplicity is neither formable nor formed; and these, again, are generally in passing without much explanation. We do get more in Book VII of the work and passages that refer back to this, and I will talk about that in a moment, but Augustine talks about divine simplicity a lot more in the De Trinitate than he ever does elsewhere, and it doesn't actually occupy much of the book because it is a major concern for him.
What of the more substantive discussions, though? In order to understand these we have to understand why Augustine is writing the De Trinitate in the first place. The De Trinitate is an attack on Arianism. It is not, as some have claimed, a speculative work, although one can perhaps say that there's always a speculative aspect to Augustine. It is a polemical work. It is frank about this, opening with an explicit statement of this intention, and the entire discussion is an argument against Arianism -- the Eunomian version of it, at least as Augustine understood it. Pinning down Eunomianism precisely is a bit tricky, but suffice it to say that the Eunomians argued that God is Unbegotten (agennetos) and perfectly simple. The Son, however, is Begotten (gennetos), and therefore cannot be God. The Father and the Son, contrary to the orthodox profession, are not consubstantial; the Son cannot even be like the Father in being. What makes the Son the Son? The fact that God communicates divine energy or operation to him, and it is in this sense that the Son is divine.
It is likewise difficult to determine how much of the Eunomian position Augustine actually knew. While Augustine does argue against various kinds of Arianism throughout his writings, in general they tend to show that he knows the heresy mostly through books. In any case, the basic positions for which Augustine is arguing in the Trinity are, first, that the Holy Trinity is the one true God, and, second, that we are not being incoherent if we accept that Father, Son, and Holy Spirit are consubstantial. To this end he argues that Scripture requires the doctrine of the Trinity (thus handling the first point) and that there is a way for someone who loves God to recognize that the rejection of consubstantiality as simply incoherent is wrong. It's noteworthy that at the very beginning he asks that his readers not read him superficially, but to be very careful that what they are attributing him is what he actually says.
Thus Augustine is only considering simplicity so far as to argue against the Eunomians in favor the Nicene thesis that Father, Son, and Holy Spirit are consubstantial and therefore one God. He also tends to raise it in particular when he is talking about the Father, Son, and Holy Spirit being equally God. It is precisely in this context that the most important discussion of divine simplicity, in Book VI takes place. As he puts it (VI.iii):
But Scripture proclaims, that "He thought it not robbery to be equal with God." Therefore any adversary of the truth whatever, provided he feels bound by authority, must needs confess that the Son is equal with God in each one thing whatsoever. Let him choose that which he will; from it he will be shown, that He is equal in all things which are said of His substance.
To explain this, Augustine immediately in the next chapter discusses an analogy. In the human mind, we have many virtues. When we attribute, say, prudence and justice to the mind, we mean different things. However, these virtues are not separable. This position, usually called the unity of the virtues thesis, is extremely common prior to the modern period. In order to have any one of the cardinal virtues, especially in full form, you have to have them all. To have prudence, you have to have justice, fortitude, and temperance; and people who are equal in prudence have to be equal in the others. How much more so, then, should divine excellences be regarded in the same way, given that the human mind is not as simple (noncomposite) as the divine substance? In the human mind, we cannot say that to be is the same as to be courageous or prudent or temperate or just. Why not? Because our minds can exist without these. This is quite important, so I will repeat it: The precise sense in which being and being wise (or just, etc.) fail to be the same in us is that we can be and fail to be wise (or just, etc.). With God, however, it is different:
Since, in the human mind, to be is not the same as to be strong, or prudent, or just, or temperate; for a mind can exist, and yet have none of these virtues. But in God to be is the same as to be strong, or to be just, or to be wise, or whatever is said of that simple multiplicity, or multifold simplicity, whereby to signify His substance.
When we attribute a divine excellence to God, then, we must do so in a way that recognizes that He is a "simple multiplicity or multifold simplicity" and that He has this excellence in such a way that He cannot possibly fail to have it. To be God is to be divinely wise, divinely just, etc.; and these are all unified, like the virtues in us, but even more perfectly. Since, however, Augustine has argued that Scripture tells us that the Son is equal to the Father, in order to be equal to the Father in one divine excellence, He must be equal to the Father in all divine excellences, precisely because the divine excellences are "simple multiplicity or multifold simplicity". Therefore the Son is consubstantial with the Father. The same thing is true of the Holy Spirit.
One might ask, however, what sense it makes to talk of "simple multiplicity or multifold simplicity" in the first place, if one is not persuaded of its coherence by the analogy with the unity of the virtues. Augustine explicitly addresses this concern by approaching the subject another way. We say creatures are not simple; so what leads us to draw this conclusion? Consider a body. We recognize that this body has parts, and that means in particular that these parts can be greater or lesser than each other, and the whole is greater than the parts. Likewise, we take color to be something different from size, and both to be different from shape. Why do we think this? Because the body can change size without changing color, change color without changing size, change either without changing shape, and change shape without changing either. Thus we conclude that bodies are composite. Now Platonist-wise, consider a spiritual substance, which will be more simple than a body. Why might we say that it is still composite? It certainly lacks the easy division into parts that bodies have; we can even say in some sense that it is whole in both whole and part, or, in other words, that the line of reasoning we used about parts and wholes fails for spiritual substances. However, it is still the case that we can take the soul to be composite, because we can recognize that it has qualities separable from each other and from itself. A spiritual substance can fail to be skillful, but become skillful; likewise, it can lose its skill. In addition, its various qualities can change with respect to each other, just as the qualities of bodies can. Thus, Augustine says, we know that spiritual substances are composite because they are changeable.
Just as the line of reasoning about parts and wholes that we used on bodies failed for spiritual substances, however, the line of reasoning about changeableness that we used on both fails for God. We can say many, many things of God, with good reason: but God is not composite, because divine excellences are equal and unchangeable, and therefore inseparable. Thus Augustine says,
His goodness is the same as His wisdom and greatness, and His truth the same as all those things; and in Him it is not one thing to be blessed, and another to be great, or wise, or true, or good, or in a word to be Himself.
It is important to be quite clear that, given the way the argument is set up, the only possible way to understand this is to take Augustine as saying that divine excellences are the same in the sense that they are equal and having one means that one cannot fail to have the others. Every one of the several passages in which Augustine says something like, "In God, to be is to be wise," must be understood in precisely this sense, because it is in every case a reference back to this argument. And in fact this becomes extraordinarily obvious: whenever Augustine mentions it, you always find that he's also talking about how God's excellences do not change and do not admit of greater or lesser.
And, of course, the whole point of this is again to argue for the consubstantiality of the Trinity. God cannot be divided into parts according to greater or less, the way bodies can; God's excellences cannot come and go; and if a Person has one divine excellence, He cannot fail to have them all. Thus if the Son and the Spirit are equal to the Father in any divine excellence, they must be consubstantial with the Father. And this, too, we find in every case.
We can easily that other comments by Augustine relevant to the account of simplicity in the De Trinitate are very similar. For instance, at one point Augustine says that we can speak substantively and relatively of God, and that God is not a subject of qualities but things like good, wise, etc., are all said of God substantively. But, again, it is clear in context that he is concerned to argue that God is not something that could be nonwise, nongood, etc.
We could go into more detail on specific passages, but it should be clear enough that Augustine's account of divine simplicity does not collapse all the divine excellences into each other. This is inconsistent with his analogy with the unity of virtues, and it is inconsistent with his claim that the divine simplicity is a "simple multiplicity or multiple simplicity", and it does not fit with the argument that he actually gives when you look at his claims in context rather than quoting them out of context.