What does it mean to pray "in Jesus' name"? Is it a magical formula that guarantees that your prayer will be heard? For example:
Dear God, please give me a new bike and a chocolate cake and a magical telephone and an elephant. Also, please kill all the bad people. In Jesus' name, Amen.
Does that prayer make more sense because it has "In Jesus' name" at the end? No, indeed not. This is the "cosmic vending machine" or "God as Santa Claus" way of understanding God, and it's pernicious and false. God doesn't act like that.
Let's consider instead the connotations of the word name. It doesn't just mean the word "Jesus" in the same way that "lonesomeday" refers to me. It's very much bound up with the identity of the individual. Think, for instance, back to the Old Testament. The supreme revelation of God's nature to the people of Israel came in the giving of his name:
But Moses said to God, ‘If I come to the Israelites and say to them, “The God of your ancestors has sent me to you”, and they ask me, “What is his name?” what shall I say to them?’ God said to Moses, ‘I am who I am.’ He said further, ‘Thus you shall say to the Israelites, “I am has sent me to you.” ’ God also said to Moses, ‘Thus you shall say to the Israelites, “The Lord, the God of your ancestors, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you”: This is my name for ever, and this my title for all generations.’ (Exodus 3.13-16, NRSV)
The name of God is who God is. It is so holy, so bound up with his entire identity, that it is never uttered by Jews. It was uttered just once a year by the High Priest in the Holy of Holies on Yom Kippur. It was immensely powerful because it was not just a word but an identity. Similarly, take Psalm 20:
Some take pride in chariots, and some in horses, but our pride is in the name of the Lord our God.
This isn't saying "we're proud that our God is called YHWH", but "our pride comes from who our God is".
This is the sense that "name" is used in the Gospel of John. It's actually used on a whole host of occasions. Here are a few of them to give a suggestion of what it connotates:
But to all who received him, who believed in his name, he gave power to become children of God (John 1.12)
Those who believe in him are not condemned; but those who do not believe are condemned already, because they have not believed in the name of the only Son of God. (John 3.18)
I have come in my Father's name, and you do not accept me; if another comes in his own name, you will accept him. (John 5.43)
But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you everything, and remind you of all that I have said to you. (John 14.26)
But they will do all these things to you on account of my name, because they do not know him who sent me. (John 15.21)
"I have made your [i.e. the Father's] name known to those whom you gave me from the world. (John 17.6)
But these are written so that you may come to believe that Jesus is the Messiah, the Son of God, and that through believing you may have life in his name. (John 20.31)
Beyond this, we might also point to the occasions where Jesus alludes to the name of God in his speech, such as 8.58: ‘Very truly, I tell you, before Abraham was, I am.’
These give, I think, a bit of a picture of what "Jesus' name" is referring to in John. It refers precisely to Jesus' identity and his purpose. "Jesus' name" is who Jesus is. And we know from the prologue to the Gospel that Jesus is "the Word made flesh". He is the one who has "made God known".
So when we pray "in Jesus' name" we are praying "according to who Jesus is", that is to say according to his nature as the revelation of God; the salvation of his people; the way, the truth and the life; the gate of salvation. We are praying according to who Jesus most fundamentally is. To pray in Jesus' name is to conform ourselves to that identity.
What does it mean, then, to ask for something in Jesus' name? I don't know precisely. But it is rooted in our Christian knowledge of who Jesus is. It is connected intimately to the fact of our salvation. It isn't a separate magical formula that gets us a special hearing.
Andrew Lincoln wrote an chapter on this subject, entitled "God's name, Jesus' name, and prayer in the fourth gospel". It can be found in a book entitled Into God's Presence: Prayer in the New Testament. I'm afraid I don't have a copy, but I read it a little while ago and it is excellent.