As I look at this question, a number of thoughts run through my mind on the matter of praying. The first is motivation. God does not look on our outward appearance/performance as much as our inner motivation. If we are merely going through the words because they are written and/or expected, then we are in the wrong ballpark. Jesus had issues with the people who were "religious" and merely performing. He chided the people who prayed in public to show off their "spirituality". In similar manner he castigated the pharisees who made a show of their religiosity. God looks on the heart of the person and not the outward appearance.
Secondly, Jesus gives us a model prayer. When the disciples had questions about praying ("Teach us to pray" (Luke 11:1), "When you pray, say: 'Father (or Our Father)....'") I think the thing that Jesus is driving home to us is that prayer is relational. It is between a Father/child. We are able to access God as we would be able to access a loving father. [I know that some people have not experienced good family relationships, but in our hearts we know what a father should be like.]
God desires to have a relationship with us. He desires that we know him (not about Him), that we come before Him in prayer--just talking it over with Him, and that we listen to what He has to say to us through His Word, the Bible.
“...in Jesus’ name”. To me, this is a recognition that as a beliver our salvation is in and through Jesus. He is the one who secured our salvation, he is the one who sustains us; he is the one who is our hope. 1 Timothy 2:5 tells us that there is ONE MEDIATOR between God and mankind and that is Jesus.
More importantly is the instruction of Jesus. It is shortly before his crucifixion and he is giving to his disciples his “last will and testament” (John 13-17). John emphasizes a number of times that Jesus told his disciples to pray in his name: