Thank you all for your thoughtful answers, but I didn't see the question fully addressed. While it's true that something does not need to be explicitly named in order for it to be described, but why is the Trinity never explained or described in the Bible? For example, God is never described as three, or three-in-one, nor does the Bible say God is the "Father, Son, and Holy Spirit." With something as important who God is, why did they not mention who God is using the Trinitarian formula?
It is in the Bible, it is both talked about, and symbolically described. Note there are plenty of passage that describe this relationship, I just have not got the time or memory to recall them all.
Jesus as God
Col 1:17 And He is before all things, and in Him all things consist.
Col 2:9-10 For in Him dwells all the fullness of the Godhead bodily; and you are complete in Him, who is the head of all principality and power.
Jesus with the Father but still God
Joh 1:1-3 In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through Him, and without Him nothing was made that was made.
2Jn 1:3 Grace, mercy, and peace will be with you from God the Father and from the Lord Jesus Christ, the Son of the Father, in truth and love.
1Jn 2:23 Whoever denies the Son does not have the Father either; he who acknowledges the Son has the Father also.
Father, Son, and Holy Spirit
Mat 28:19 Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
Rev 5:6 And I looked, and behold, in the midst of the throne and of the four living creatures, and in the midst of the elders, stood a Lamb as though it had been slain, having seven horns and seven eyes, which are the seven Spirits of God sent out into all the earth.
The Seven Spirits of God, is the Holy Spirit. See:
Zec 4:10 For who has despised the day of small things? For these seven rejoice to see The plumb line in the hand of Zerubbabel. They are the eyes of the LORD, Which scan to and fro throughout the whole earth." .... these are described as Zec 4:14 .... the Lord of the whole earth."