In the name of X means in the authority of X.
Acts 3:
Note that the asking in Jesus' name is sandwiched between the two indwellings.
For us, we need to pay attention to the Paraclete in us. Ask according to Him. Then whatever we ask will be done.
"In Jesus' name" is not some kind of magical formula. That's why there is no example of prayer in the NT that ends with "in Jesus' name", Acts 9:
Don't just mindlessly end a prayer with "in Jesus' name" as if it is a formula. Can you in clear conscience say that you have prayed as Christ's representative on earth? Do you have the authority of Jesus to pray that prayer? Have you prayed according to the will of God?
See also When you pray, say: FATHER.
Acts 3:
Earlier after the Last Supper, Jesus told his disciples in John 14:6 But Peter said, “I have no silver and gold, but what I do have I give to you. In the name of Jesus Christ of Nazareth, rise up and walk!”
Cambridge Bible for Schools and Colleges:13 I will do whatever you ask in my name, so that the Father may be glorified in the Son.
It is not a formula.Anything that can rightly be asked in His name will be granted; there is no other limit. By ‘in My name’ is not of course meant the mere using the formula ‘through Jesus Christ.’
Merriam-Webster in someone's name:Rather, it means praying and working as Christ’s representatives in the same spirit in which Christ prayed and worked,—‘Not My will, but Thine be done.’ Prayers for other ends than this are excluded; not that it is said that they will not be granted, but there is no promise that they will.
John affirmed this understanding in 1 John 5:something is done with the authority of a specified person
Let's check the context, John 14:14 And this is the confidence that we have before Him: If we ask anything according to His will, He hears us.
The Father dwells in the Son to enable the Son to speak with the authority of the Father.The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works. 11 Believe me that I am in the Father and the Father is in me, or else believe on account of the works themselves.
i.e., if we ask with the authority of Jesus, it will be done.12“Truly, truly, I say to you, whoever believes in me will also do the works that I do; and greater works than these will he do because I am going to the Father. 13 Whatever you ask in my name, this I will do, that the Father may be glorified in the Son. 14 If you ask me anything in my name, I will do it.
The Paraclete dwells in us to enable us to speak with the authority of the Holy Spirit.15“If you love me, you will keep my commandments. 16 And I will ask the Father, and he will give you another Helper [Paraclete], to be with you forever, 17even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you.
Note that the asking in Jesus' name is sandwiched between the two indwellings.
For us, we need to pay attention to the Paraclete in us. Ask according to Him. Then whatever we ask will be done.
"In Jesus' name" is not some kind of magical formula. That's why there is no example of prayer in the NT that ends with "in Jesus' name", Acts 9:
Peter prayed/commanded in Jesus' name without explicitly using the word "in Jesus' name", i.e., Peter prayed and acted as a representative of the authority of Jesus. Acting in Jesus' name is more important than mouthing the formula. Today, we Christians have gotten it the other way around and the formula has become meaningless.40 Peter sent them all out of the room; then he got down on his knees and prayed. Turning toward the dead woman, he said, “Tabitha, get up.” She opened her eyes and seeing Peter she sat up.
Don't just mindlessly end a prayer with "in Jesus' name" as if it is a formula. Can you in clear conscience say that you have prayed as Christ's representative on earth? Do you have the authority of Jesus to pray that prayer? Have you prayed according to the will of God?
See also When you pray, say: FATHER.