Many Christians learn, directly or indirectly, to say, "In Jesus' name, Amen" at the end of their prayers. Why do we do it? Most probably do it without giving it much thought. It's just the way prayer is done. Actually, while we don't have to say it (we really don't) it is meaningful when we learn the significance of those words.
In the ancient world a person's name (or a god's) stood for the person. When we say, "Bless the name of the Lord," we are really saying, "Bless the Lord." In the Bible a person's name stood for his character as well. We still say today, "I know that business. It has a good name in the community."
To say, "In Jesus' name," we mean, "In light of the person that Jesus is, in light of what he accomplished on the cross, we have confidence to say 'Amen.'" Amen is an affirmation which means so be it. Amen is the confidence to believe that our prayer will be answered.
Christianity is all about Jesus. We are "in Christ." We receive grace and mercy from God the Father because we come "in the name of" his Son. All answered prayer happens because of what Jesus deserves, not what we deserve.
Consider this passage:
I wanted to visit you on my way to Macedonia and to come back to you from Macedonia, and then to have you send me on my way to Judea. Was I fickle when I intended to do this? Or do I make my plans in a worldly manner so that in the same breath I say both "Yes, yes" and "No, no"? But as surely as God is faithful, our message to you is not "Yes" and "No." For the Son of God, Jesus Christ, who was preached among you by us—by me and Silas and Timothy—was not "Yes" and "No," but in him it has always been "Yes." For no matter how many promises God has made, they are "Yes" in Christ. And so through him the "Amen" is spoken by us to the glory of God. (2 Cor 1:16-20 NIV)
Paul said that even if the Corinthians wrongly thought his word was unreliable, Jesus' word certainly is not. God answers our prayer because of Jesus. And that's why we say, "In Jesus' name, Amen."