Let's jump back to the river toponyms for a bit. Recently I dived into a book of Hóman Bálint, a historian who served as a Minister of Religion and Education for about nine years in the interwar and WWII era. This book offers a bit of addition to the various versions of the Don.
Dnieper = Dana-per = "rear river"
Dniester = Dana-ster = "first river" or "near river"

Maybe we could take a look at the Greek names
Don = Tanais - a Greekified form of its local name; Plutarch (or someone else using his name) called it Amazon river or Amazonian.
Dnieper = Borysthenes - the Internet Encyclopedia of Ukraine says the name has local origin, and not Greek
Dniester = Tyras - also a Greekified name of Scythian origin, tura supposedly means "rapid"
Danube = Istros - in Latin: Ister; again local in origin, supposedly the Thracian word means "rapid" again.
Thracians also called the Dniester Istros/Ister, and its name is a combination of Don + Ister. I know this seemingly contradicts the first statement but these are just a bunch of speculations. It could be Ister also means "first" in Scythian. Or whatever.
These Greek names also identified cities as well, which laid about the mouth of those rivers.
Note: close to the city called Istria, there's a small river with the same name, flowing into the Lake Istria. Today a Romanian village lays nearby, called Istria.