In Christian orthodoxy, we believe that God is simple. To say that God is simple is to say that He is "without parts," not a composite being. Anything that is composite, being made up of parts, can be "dismantled" into parts. For example, a chair is not simple, for any part of the chair can be cut off to form 2 or more parts. A human being is not simple, since we can remove a hand and we have a person (without one hand) and a detached hand. Basically, almost anything that exists is composite, since it can be broken further. Even an atom can be broken up into electrons, protons and neutrons, and those can be broken up even further.
The point here when applied to God, other than to say that God is totally unlike the creation, is that God cannot be made deficient. One gets God, or one gets nothing. Also, since one cannot separate anything of God from God, God's being is His attribute, who is He is what He is described as in full. Or, to be more technical, God's essence is His attributes. Since God is indivisible, God's will is one. His will is His attributes is His being, and there is no plurality in His being.
Of course, God is triune, which means that in this one being there are three persons, all coequal and all fully God. It is a lofty truth which stretches our minds, and we can never fully comprehend this truth. But throughout the centuries, we have come up with theological concepts in order to safeguard our thinking about God from veering into heresy. God is both one and three, but obviously anything cannot be both one and three in the same way, so we come up with the language of essence and persons to safeguard the truth of the one and the three. We especially use the word "person" (προσωπον; personna) because there lies the closest analogue we can find in seeing how humans behave as persons. A person acts and interacts, and the different persons of the Trinity act and interact with the world and God's people just like how persons do. By definition, persons are individuals such that Person A is not Person B. If God the Father says to Jesus "This is my beloved Son," it is God the Father who is saying this, not God the Son or God the Holy Spirit. To say otherwise is to move towards Modalism, whereby the one God as the Father says "This is my beloved son" to himself as the Son, which is of course heretical.
If the persons of the Trinity are indeed persons, then they are persons. Persons in order to act and interact will, and then they act on that will to effect what they will should be done. In other words, a real person must have a real will of his own. To go back to that example, does God the Father will to say "This is my beloved son"? Yes, but does God the Son say that? No. God the Son did not say "This is my beloved Son," and therefore He did not will to say it, for if He willed to say it, He would have said it. Different persons necessitate distinct wills, for otherwise they are not real persons.
But one can object that my example comes from Jesus in His incarnation. Yes, so let's run with that. Are those who reject distinct wills of the person willing to therefore say, in line with their "exception" clause of the incarnation, that during the incarnation at least, Jesus actually have a distinct will from the Father? But oh, it is a human will. Yes, Jesus has both a human and a divine will, but that is besides the point. Whichever will is operative is the one acted on. When Jesus knew Nathanael even before He actually saw him (Jn. 1:48), that was the divine nature and divine will at work. When Jesus said, "I thirst," that was the human nature and will at work. So are we to suppose that Jesus' divine will would be wanting to say "This is my beloved son," (since there is one will) but the human will prohibited Jesus from saying the words? May it never be!
So yes, according to the doctrine of simplicity God has one will. Yet I hope it can be seen that, for the persons of the Trinity to be actual persons, each of them must have distinct wills. One will and three wills, and both are true? Yes, just as God is both three and one, His will is both three and one. God's will, as an attribute of God is identical to His being. But each persons must also have a distinct will in order to be persons. In explaining the Trinity, we say that God the Father is God, God the Son is God and God the Holy Spirit is God, but the Father is not the Son is not the Holy Spirit. Likewise, we should say that the will of the Father is the will of God, the will of the Son is the will of God, and the will of the Holy Spirit is the will of God, yet the will of the Father is not the will of the Son is not the will of the Holy Spirit.
To be sure, these are not separate autonomous wills, but rather they cohere and work together, for God is one. So as all are the will of God, so whatever God wills, the persons also will. There is therefore an objective similarity between the wills of the persons, but a subjective distinction between them based upon who they are as persons.
It has been said that Western theology tends towards collapsing the three persons into the one essence, while Eastern (Orthodox) theology tends towards over-emphasizing the three distinct persons. It seems perhaps plausible that the current rejection of any form of eternal submission (NOT subordination) of the Son stems from the same Western inclination towards the one essence at the expense of the three persons.