With the NT adopting the Greek-ized form of the saviour's name, the signficance of Joshua taking the people into the promised land is obscured: I prefer to think of the Messiah as Joshua of Nazareth: closer to the truth!
But if we were going to render our Lord's earthly name into contemporary style, it would be as the title of this post: Joshua Davidson! It doesn't quite work liturgically, but there you are!