We don’t know anything about Nun. Joshua is called the son of Nun ten times in the book (Joshua 2:1, Joshua 2:23; Joshua 6:6; Joshua 14:1; Joshua 17:4; Joshua 19:49, Joshua 19:51; Joshua 21:1; Joshua 24:29). Presumably his father was someone well known.
1 After the death of Moses the servant of the LORD, the LORD said to Joshua the son of Nun, Moses’ assistant,