It’s important to recognize the model prayer—the prayer of Jesus, the prayer that Jesus taught his followers to pray—does start: “Our Father which art in heaven, hallowed be Thy Name” (Matt. 6:9). And I think that the recognition here is that, first and foremost, our desire, what we really care about, is that God’s Name be made holy. Our daily lives should radiate a far greater commitment to God’s nature and His holiness than to our own needs.
So to pray, “hallowed be Your Name,” is to pray that God be given the unique reverence that His holiness demands, that God’s Word be preached without corruption, that our churches be led by faithful pastors and preserved from false prophets, that we’d be kept from language that profanes the name of God, and that our thought lives remain holy, that we cease from seeking honor for ourselves but ask instead that God’s Name be magnified.
In saying this there’s nothing wrong with using the names of God as opposed to the titles for God. There’s nothing wrong with addressing our Lord and Savior Jesus Christ and thanking Him for His sacrificial death on our behalf. There’s nothing wrong with thanking the Holy Spirit for empowering us as we pray, as we witness, as we provide for our families. So the standard is we pray to the Father, in the Name of the Son (or through the Son), by the power of the Holy Spirit. But Jesus Himself invites us to pray to Him in John 14:14.
So there is no set formula. We pray to one God revealed in three persons, who are eternally distinct.
—Hank Hanegraaff
For further related study, please see the following:
What Are Some Secrets to Effective Prayer? (Hank Hanegraaff)
The Prayer of Jabez or the Prayer of Jesus (Hank Hanegraaff
Prayer of Jesus: A Discussion Between Hank Hanegraaff and Lee Strobel
Is the Trinity Biblical? (Hank Hanegraaff)
[Answer taken from: “How Should Christians Start Their Prayers? Can We Pray to Jesus and the Holy Spirit?”]