Misunderstanding: "The Father, the Son, and the Spirit are just different titles for Jesus, or three different ways that God has revealed himself."
Truth: The Bible clearly shows that the Father, Son, and Holy Spirit are distinct persons.
Some people think that the doctrine of the Trinity contradicts the truth that there is only one god. They argue that Jesus alone is the one true God, and therefore that Jesus is "the name of the Father and the Son and the Holy Spirit" (Matt. 28:19), and not just the name of the Son. While it is certainly true that there is only one God, we must allow the Bible to define what this means. And the Bible makes it quite clear that the Father, Son, and Holy Spirit are distinct persons.
The Father sends the Son (Gal. 4:4; 1 John 4:14)
The Father sends the Spirit (John 14:26; Gal. 4:6)
The Son speaks, not on his own, but on behalf of the Father (john 8:28; 12:49)
The Spirit speaks, not on his own, but on behalf of Jesus (John 16:13-15)
The Father loves the Son, and the Son loves the Father (John 3:35; 5:20; 14:31)
The Father and the Son count as two witnesses (John 5:31-32; 8:16-18)
The Father and the Son glorify one another (John 17:1,4-5), and the Spirit glorifies Jesus the Son (John 16:14)
The Son is an Advocate for us with the Father (1 John 2:2; Greek, parakletos); Jesus the Son sent the Holy Spirit, who is another Advocate (John 14:16, 26)
Jesus Christ is not the Father, but the Son of the Father (2 John 3)
In Matthew 28:19, Jesus is not identifying himself as the Father, Son, and Holy Spirit. He is saying that Christian baptism identifies a person as one who believes in the Father, in the Son whom the Father sent to die for our sins, and in the Holy Spirit whom the Father and the Son sent to swell in our hearts.