By definition the Trinity doctrine teaches that there is only one God. Nevertheless, there are those who assert that the Trinity is really teaching three separate gods. They claim it is either impossible for God to exist in three persons and/or that the Trinity is really borrowed from pagan three-god figures. Many add that a person is by necessity an individual being. Therefore, they conclude, that the Trinity really teaches three gods.
The problem with this criticism is that it denies the very nature of the doctrine. First of all, Trinitarianism by definition denies that there is more than one God. It is clearly monotheistic in spite of what the critics want to claim.
Second, there is a word used to describe a unity of three separate gods. It is the word "triad." A triad is not a trinity. A triad is three separate gods -- as in Mormonism. A Trinity is one God in three persons. A triad is polytheistic. A trinity is monotheistic.
Third, there is no logical reason to deny the possibility that three persons can exist in one God. Critics may not like it, but it is not a logical impossibility. God is infinitely complex and we cannot understand His vastness nor simply claim He can't exist in three persons. Instead, we should look at the Bible to see what it says about God and see if the Trinity is taught. But, that is another subject.
Theologians admit that the word "person" is not the perfect word to use because it carries with it the idea of individuals who are different beings. We are familiar with this limitation because it presents a problem when we use the term "person" to describe the Father, the Son, and the Holy Spirit. But this is what we must use when we see the Bible speaking of the Father, the Son, and the Holy Spirit... each are called God, each speak, and each have a will. They exhibit attributes of personhood. We describe what we observe and are forced to use words with which we are familiar. "Person" is just such a word. It is not necessary for each person to exist as an individual being.
And fourth, trinities are known and accepted by people as observed in nature. By analogy we see that creation itself is Trinitarian. Time is past, present, and future. There are not three times. Each part of the whole of time is by nature time yet there are not three times but one. Likewise, space is height, width, and depth. Matter is solid, liquid, and gas. The Bible says that God's invisible attributes are made known in creation
Rom. 1:20: "For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made."
When the critics of Trinitarianism say it really teaches three gods, they demonstrate their lack of understanding of the doctrine and they either purposefully or mistakenly confuse it with something it is not. Trinitarianism denies and opposes the idea that there is more than one God. It is by definition, monotheistic.