Where does the Bible explain the doctrine of the Trinity, or even use the word “Trinity”?

Although the word "Trinity" is not there, the teaching is. Here is one of the texts that converted me from Araianism to Trinitarianism:

Matthew 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:

A name in scripture is more than a label, its a description of what is named, revealing its contents or its effects. Name is singular, yet three are subsisting equally in that one name.

Clearly...

God is One in Three Persons, in blessed Trinity.

Proverbs 30:
4 Who hath ascended up into heaven, or descended?
who hath gathered the wind in his fists?
who hath bound the waters in a garment?
who hath established all the ends of the earth?

what is his name, and what is his son's name, if thou canst tell?

5 Every word of God is pure: he is a shield unto them that put their trust in him.

6 Add thou not unto his words, lest he reprove thee, and thou be found a liar.

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The times of this ignorance God winked at; but now commandeth all men every where to repent:

Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.-kjv