Jesus encourages us to pray in His name. “Whatever you ask in My name, this I will do, that the Father may be glorified in the Son. If you ask anything in My name, I will do it” (John 14:13-14). What, then, does it mean to pray in Jesus’ name? We often use it as a tag at the end of our prayers, “in Jesus’ name. Amen.” There’s nothing wrong with this, but to pray in His name is more than that. Saying “in the name of Jesus” is not some magical incantation to get Him to do what we want, just as the pagans did in antiquity with their false gods. Famous philosopher and theologian, Søren Kierkegaard (1813-1855), says the following about praying in Jesus’ name:
To pray “in the name of Jesus” may perhaps be explained most simply of all in this way. A magistrate orders this and the other thing in the name of the King. What does that mean? In the first place it means: I myself am nothing, I have no power, nothing to say from myself—but it is in the name of the King. Thus to pray in the name of Christ means: I dare not approach God without a mediator [1 Timothy 2:5]; if my prayer is to be heard then it will be in the name of Jesus, what gives it strength is that name. Next, when a magistrate gives a command in the name of the King, it naturally follows that what he commands must be the King’s will, he cannot command his own will in the king’s name. The same thing is true of praying in the name of Jesus, to pray in such a way that it is in conformity with the will of Jesus. I cannot pray in the name of Jesus to have my own will; the name of Jesus is not a signature of no importance, but the decisive factor; the fact that the name of Jesus comes at the beginning [or end] is not a prayer in the name of Jesus; but it means to pray in such a manner that I dare name Jesus in it, that is to say think of Him, think of His holy will together with whatever I am praying for. Finally when a magistrate gives an order in the name of the King it means that the King assumes the responsibility. So too with prayer in the name of Jesus; Jesus assumes the responsibility and all the consequences, He steps forward for us, steps into the place of the person praying.quoted in Schumacher, 10-11; emphasis mine
In short, think on who it is to whom you are praying: Christ the King. When you pray in His name, you pray with the desire of His will, not your own. For the King always does what is best and most wise for His people, even if they do not see it that way or necessarily like it. Praying in His name, therefore, is foremost the humble disposition that trusts in the will of the King of the universe. Praying in His name trusts in His will as Mediator to intercede for us before God the Father, whose will always matches the Father’s will (John 6:38-40). Therefore, when you say, “in Jesus’ name,” be sure the meaning of those words match the desire of your heart—that His good and gracious will be done, which may not always match your will. Matching your heart’s desire with the will of Christ does not guarantee it will happen, but it will guard you from vast disappointment and doctrinal error (e.g., “God isn’t listening to me”). If His will so happens to match yours, consider it a happy accident. If His will does not match your own, praise Him for His wisdom and mercy.
Schumacher, Frederick J., and Dorothy A. Zelenko. For All the Saints: A Prayer Book For and By the Church. Volume I, Year 1: Advent to the Day of Pentecost. Delhi, NY: The American Lutheran Publicity Bureau, 2003.