First, note the larger context ...
[John 16:19-28 NLT]
19 Jesus realized they wanted to ask him about it, so he said, "Are you asking yourselves what I meant? I said in a little while you won't see me, but a little while after that you will see me again. 20 I tell you the truth, you will weep and mourn over what is going to happen to me, but the world will rejoice. You will grieve, but your grief will suddenly turn to wonderful joy. 21 It will be like a woman suffering the pains of labor. When her child is born, her anguish gives way to joy because she has brought a new baby into the world. 22 So you have sorrow now, but I will see you again; then you will rejoice, and no one can rob you of that joy. 23 At that time you won't need to ask me for anything. I tell you the truth, you will ask the Father directly, and he will grant your request because you use my name. 24 You haven't done this before. Ask, using my name, and you will receive, and you will have abundant joy.
25 "I have spoken of these matters in figures of speech, but soon I will stop speaking figuratively and will tell you plainly all about the Father. 26 Then you will ask in my name. I'm not saying I will ask the Father on your behalf, 27 for the Father himself loves you dearly because you love me and believe that I came from God. 28 Yes, I came from the Father into the world, and now I will leave the world and return to the Father."
v.23 When Jesus returns (after the resurrection), they will not need to ask Him for anything.
v.23 They will ask God the Father directly and God will “grant your request” in Jesus name.
v.24 Ask using Jesus name and they will receive.
v.24 What they will HAVE is abundant joy.
v.26 Jesus will not ask for them, they will ask God directly.
v.27 God will listen because God loves THEM!
So now that we have some context, time to address your question:
What does it mean to ask in Jesus' name?
First, Jesus never said that God would become your genii, granting everything that YOU want. The promise was that God would deliver whatever was requested in Jesus name by those who loved and believed Jesus and are loved by the Father.
I see no reason to make the phrase “in Jesus name” more complicated than necessary. It is not a magic incantation that you chant to get whatever you wish for. At work, I am called to frequently represent corporate clients in land development deals. I frequently receive a paper naming me as the “agent of record” with the authority to speak for the company and sign applications related to the project that they have hired me to take care of. All I do is done “in their name” which means that I am acting with their authority to pursue their interests. While I am acting with their authority and in their interest, “in their name”, I have tremendous power to make decisions and spend money and bind others to agreements that are far beyond my innate resources. I don’t have $1 million to pay for roadway improvements, but I can promise that the money will be paid and ... those in whose name I am operating pay it.
So to ask in Jesus name, implies that we are operating under Jesus’ authority and looking out for Jesus’ goals and interests. In such a case, we have a promise that God the Father loves us and will not leave us hanging in any project that He has assigned us to.
[Ephesians 2:10 NLT] 10 For we are God's masterpiece. He has created us anew in Christ Jesus, so we can do the good things he planned for us long ago.
So that is what I think “in Jesus name” means.