Although they do seem to have similar Latin-Germanic roots, if one can decipher the ancient etymological book here: http://runeberg.org/svetym/1298.html
There are multiple rivers with "älv" as a suffix in Sweden, among them the biggest and most economically/historically significant. This means that any possessive formed by "älv-" automatically would refer to a river.
If you'd set your Swedish language fantasy world where there's a place called "Älvdalen", readers would be confused. It would be like calling Minas Tirith Stockholm.