The little notes at the bottom of my bible in the Gospel of Mattew, indicate that Jesus or Ἰησοῦς is the Greek for of the name Joshua. The name יְהוֹשֻׁעַ or Yehoshua in Hebrew means "Yahweh is salvation" and in Greek and most Orthodox churches, Joshua is almost always rendered "Jesus son of Nun" in the Greek to differentiate them.
Now a lot of the Old Testament can be taken as Object Lesson for what was and is to come; so I'm wondering what sort of parallels should be drawn between the two.
Joshua was one of the twelve spies sent by Moses to report on Canaan and only he and Caleb gave reports which were optimistic in Numbers 13 & 14 and ultimately he would be the one to lead the nation of Israel in conquest of the land.
Maybe there is a parallel between Jesus in Joshua in that Jesus was sent to make a report; not on the condition of the enemy but of the soon to be arriving Kingdom of God. It could also be said that Joshua's job was to conquer the land of Canaan and to smash strongholds. Jesus' job was conquer sin and also to smash strongholds, though maybe that's too long a bow to draw.
Maybe there really isn't any parallel to be drawn, maybe Jesus name יְהוֹשֻׁעַ simply means "Yahweh is salvation" and that's that. It doesn't need to be any more complicated than that does it?