that you may come to believe that Jesus is the Messiah, the Son of God, and that through this belief you may have life in his name.
It's a double purpose, reflecting the two fundamental beliefs of the Christian:
Jesus is the Messiah, the Son of God.
Through the belief that Jesus is the Messiah, you may have life in His name.
These beliefs can be socially awkward, and the ways in which Christians betray and deny them are legion.
It occurs to me, though, that the faithful Christian will have life in Jesus' name, regardless of whether Jesus is the Messiah. It was a participation in His own life with the Father that Jesus promised His disciples. This is a promise that will necessarily be kept: if Jesus rose from the dead, so will His disciples; if He didn't, neither will they.
Whatever happened to Jesus will happen to us; whatever He is like now is what we shall be like. Christian and non-Christian alike should agree on these points.
The faithful Christian, then, is like the young man at the end of "The Lady or the Tiger?," who, "with a firm and rapid step" and "[w]ithout the slightest hesitation" opened the door his lover had signaled him. Whatever lies beyond the door, Christ has passed through ahead of us, and it is Christ Whom we follow, because it is Christ Whom we want.