That's a diaeresis, not an umlaut. Same symbol but different phenomena. An umlaut is a sound shift in a vowel to make it more like another vowel. For example in Icelandic a word like "Katla" will decline the final "a" to "u," which then causes the first "a" to become "ö". The a -> ö shift is umlaut. A diaeresis, however, marks a vowel that is pronounced separately from an adjacent vowel instead of as a diphthong.
The letter Ä is a separate letter in Swedish and many other languages. It is not just an A with an umlaut mark or a diaeresis. The Ä in Älv is not a shifted vowel.
For example, some style guides still call for cooperate to be spelt as coöperate (most notably, The New Yorker), but this has largely fallen out of fashion.
