“Uz.” The land of Uz (cp. Job 1:1) was almost certainly named after him. The exact boundaries of Uz are unknown, but the area was east of the Jordan River and seems to include some of Edom to the south and extend all the way north into Aram (called Syria today).
“Buz.” The land of Buz was also near Edom, but like Uz, the exact boundaries are unknown. Jeremiah 25:23 puts it close to Tema and Dedan. Elihu in the book of Job was a Buzite (Job 32:2). The Assyrian records of King Esar-haddon show he invaded Bazu and Hazu, and Bazu might be the “Buz” of the Bible. The Assyrian records show Bazu was full of snakes and scorpions, which would fit the desert territory near Edom (and also fit with the fact that when the Israelites were traveling through Edom the people were bitten by venomous snakes; Num. 21:4-9).