"In the name of" means that we have Jesus' authority to pray to the Father. It doesn't just mean that we use his name in our prayers.
Acts 19:13-16 shows someone using Jesus' name. But more than just using his name is needed: "Then some of the itinerant Jewish exorcists undertook to invoke the name of the Lord Jesus over those who had evil spirits, saying, “I adjure you by the Jesus whom Paul proclaims.” Seven sons of a Jewish high priest named Sceva were doing this. But the evil spirit answered them, “Jesus I know, and Paul I recognize, but who are you?” And the man in whom was the evil spirit leaped on them, mastered all of them and overpowered them, so that they fled out of that house naked and wounded."
Only children of God can rightly claim the authority of Jesus' name. Jesus said to pray "our Father". Not all people are children of God. (1 John 2:29-3:1)
Ephesians 2:18 "For through [Christ] we both have access to the Father by one Spirit."
Those who do not have the Holy Spirit have no access to the Father. Romans 8:8-16 shows that only those who have Christ dwelling in them, who are born again, are children of God. see also John 1:12.