To PRAY "in the name of Jesus" may perhaps be explained most simply 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 for 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, 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 is not 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 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.
Kierkeegaard, Soren, Journals, trans Alexander Dru (1938), pp 974.