I don't ever remember being taught or believing in three separate and distinct persons in the Godhead. Trinitarianism and Monotheism are two entirely opposite beliefs. The belief that there are three separate persons in the Godhead, namely the Father, the Son, and the Holy Ghost is the most widely accepted definitioon of the word trinity. Separate and distinct means "not the same". Therefore, when we speak of the "trinity", we are speaking of three divine persons, each having His own personality, thoughts, etc.
If this definition is acceptabe, the term trinity would constitute a three-part Godship, or a three-God partnership. If these divine persons are coequal, coeternal, coexistent as it is commonly believed, the we have some questions to answer. Coeternal means each is as old as the other which would make the Son as old as the Father. If Jesus existed in eternity as the Son apart from the Father, then who was His mother? Common reasoning requirres that to have a Father, one must also have a mother. How did God come about having a Son in eternity? If God created Him, then there was a space of time when God was not the Father, which would necessitate a differentation of ages. See where this all can lead?
I think most likely the term, "Trinity" wasn't coined until the time of Justin Martyr and Tertullian, (who probably was the one who came up with the term), and Tatian. No doubt there were others.
Justin Martyr was the first prolific writer to clearly teach a plurality within the Godhead. He even numbered them, saying, "We reasonably worship [Jesus Christ], having learned that He is the Son of the true God Himself, and holding Him in the second place, and the prophetic Spirit in the third."11 Again he said, "There is … another God and Lord subject to the Maker of all things; who is also called an Angel, because He announces to men whatsoever the Maker of all things-above whom there is no other God-wishes to announce to them. … He who is said to have appeared to Abraham, and to Jacob, and to Moses, and who is called God, is distinct from Him who made all things-numerically, I mean, not (distinct) in will."
Tertullian (150-225) was the first to speak of God as a trinity, and as three persons in one substance. God is "the ‘Trinity,which consists of three persons…. God is one only substance in three coherent and inseparable (Persons)’ (12). … The Father and the Son are ‘two separate Persons; , two different Beings, and distinct but not separate. The Son is ‘another’ from the Father on the ground of Personality, not of Substance-in the way of distinction, not of division.
Trinitarianism is inconsistent in the light of the Scriptures...
Isaiah 44:6 (KJV) Thus saith the LORD the King of Israel, and his redeemer the LORD of hosts; I am the first, and I am the last; and beside me there is no God.
Revelation 1:8 (KJV) I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty.
Revelation 1:11 (KJV) Saying, I am Alpha and Omega, the first and the last: and, What thou seest, write in a book, and send it unto the seven churches which are in Asia; unto Ephesus, and unto Smyrna, and unto Pergamos, and unto Thyatira, and unto Sardis, and unto Philadelphia, and unto Laodicea.
There are many others. Trinitarianism is also inconsistent in it's logic. Coequality of two or more divine, almighty persons is illogical. The doctrine of Father and the Son being coeternal is illogical inasmuch as it requires the Son to be as old as the Father and the offspring to be the same age as the original. In addition, there's a problem in that it has divine person number one (the Father) and divine person number three (the Holy Ghost) both the father of divine person number two (Jesus).
There is but one Lord, one faith and one baptism. One God who sits on the throne throughtout eternity whose name is Jesus.