Some folks question the need for a mediator between themselves and God. They wonder why they should pray 'in Jesus name' and why they would need some go-between to broker their relationship with God. The fact is, every relationship needs a mediator in order for there to be any meaningful communication.
There needs to be two things present for real communication to exist, 1. A medium of communication 2. A standard of communication.
Everyone communicates using a language of some sort: sign language, body language, French, German, English etc. By far the best means of communication is some language made up of words. It's no accident that John 1 describes Jesus as the Word become flesh. Jesus is God's language.
If you wish to communicate with a French speaker (as an English speaker) either you have to learn French or she must learn English (or you find an interpreter who speaks both languages). With God, however, you must speak his language in order to communicate with him. And that language is taught and exemplified through Jesus.
Now the standard. 1 John 3: 16 says, 'This is how we know what love: Jesus Christ laid down his life for us.' We might like to think that love comes naturally. But there is hardly anything we do that isn't learned or taught from speech and walking upright to socially acceptable behaviour and relationships. The tragic cases of feral children prove that there are a great many things we must learn in life, and one of those things is how to love. Suffice it to say, our world has many ideas of what love is and while an accurate definition of love is hard to find, the practice of an accurate definition is even harder to find. So Jesus came to show us how by being love itself.
One might react to this idea with a, 'But that's a ridiculously high standard! Who can live up it?'. Yes, it is a high standard 'laying down' one's life, but perhaps our general standard of love is also just very, very low.
Even as individuals we have our own personal standards for relationships and communication therein. We won't tolerate certain kinds of behaviour from others and despise being spoken to in a certain tone (condescending or demanding perhaps?), and may even choose to avoid usage of certain words in our speech. God is no different - he won't tolerate lies, for example. If we are to use The Bible as our standard and God 'speaks love' and 'God is love', then God's language is patience, forgiveness, gentleness, joy, mercy, gratitude, faith, hope and other virtues.
Praying 'in Jesus name' may have more to do with depending on his example, sacrifice and guidance in speaking/being the language of God rather than some legal formality at the end of our prayers.