When Did Moses Give Joshua His Name?

How could Moses be said to have given Hoshea the name Joshua in Numbers 13:16 when he has already been referred to as “Joshua” in Exodus 17:9 and 24:13?

There is no difficulty here, for the final composition of Exodus by Moses undoubtedly occurred toward the end of the forty years' wandering. Even though Joshua may not have acquired the name from Moses until later in the journey from Egypt to Canaan, nevertheless in retrospect it would have been only natural to refer to Joshua by the name he bore at the time Exodus was composed by Moses. It should be added that Yehosua‘ ("Jehovah is salvation") is virtually the same name as Hosea‘ ("salvation"), both being derived from the root yasa‘.

–Dictionary of Bible Difficulties