Exode 17:9

And Mosheh said to Jehoshua, Choose such men as are strong in the precepts, and victorious in fight; and go, under the Cloud of glory, and set battle in array against the hosts of Amalek. Tomorrow I will stand, prepared with fasting, with the righteous fathers of the chiefs of the people, and the righteous mothers who are like the hills, with the rod with which the miracles have been wrought from before the Lord, in my hand.

AND MOSES SAID TO JOSHUA. It would appear from here that from the day he came before him, Moses called him Joshua, and so it is also written: And Joshua heard the noise of the people. Scripture which states in the case of the spies, And Moses called Hoshea the son of Nun, Joshua, must then be referring to the beginning, [when Joshua first came to minister before him]. The verse informs us that this Hoshea the son of Nun, who was chosen to be among the spies, is the same one that Moses called Joshua. Our Rabbis commented [that Moses gave him this name of Yehoshua, which is a compound of Y-ah (G-d) and hoshea (help), because] he in effect prayed for him, “May G-d help thee that thou mayest not follow the [evil] counsel of the spies.” The intent of this comment is to state that because of this event of which Moses knew in advance, i.e., that Joshua was destined to go with the spies, he called him by that name [Yehoshua — Joshua] at the outset. We may also say that at that time [when the spies were chosen], Moses designated that name in front of the assembly, i.e., that his name henceforth be not Hoshea but Joshua.
The reason that Moses commanded Joshua to fight with Amalek was so that he [Moses] might pray with the raising of hands on the top of the hill. He went up there so that he might see the Israelites engage in battle and train his sight on them to bring them blessing. They too, upon seeing him with his hands spread heavenward and saying many prayers, would have trust in him, and they would thus be endowed with additional valor and strength.
In Pirke d’Rabbi Eliezer, we find additionally: “All Israel went outside of their tents, and they saw Moses kneeling on his knees, and they did likewise. He fell on his face to the earth and they did likewise. He spread his hands heavenward, and they also did so. [From here, you learn the principle that] as the public reader of prayers recites, so do all the people respond after him. And thus the Holy One, blessed be He, caused Amalek and his people to fall by the hand of Joshua.” But if so, [i.e., if Moses’ hands were spread heavenward], the sense of the expression, with the rod of G-d in my hand, must be that when Moses went up to the top of the hill and saw Amalek, he stretched forth his hand with the rod to bring down [upon the Amalekites] strokes of pestilence, the sword and destruction, just as it is said in the case of Joshua: Stretch out the javelin …