For this access to be available to the disciples, certain conditions must be met: they must abide in Jesus; His words must abide in them; they must bring forth good fruit. To this last point, it suggests that their prayers should be tied to their mission.
Jesus spoke often about “My name.” for example, receive a little child in “My name”; do a miracle in “My name”; give a cup of water in “My name.” Often in the Bible, “name” is a synonym for the bearer. We see in the Gospels that the name of Jesus has miraculous power within itself:
Luke 10: 17 Then the seventy returned with joy, saying, “Lord, even the demons are subject to us in Your name.”
Jesus also cautions not to take this idea too far. His name is not a magic formula or incantation:
Matthew 7: 21 “Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of My Father in heaven. 22 Many will say to Me in that day, ‘Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?’ 23 And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’
Yet, for His disciples – and especially after Jesus’s death and Resurrection – the name of Jesus offered special power. There are many accounts of miracles performed in Jesus’s name in the book of Acts: for example, in the name of Jesus Christ, rise up and walk.
