Umlauts are the vowel with dots, not just the dots.

In German the common word for "vowel" is "Vokal," but an older less common word is "Selbstlaut" (selbst = "self" or "by oneself"). "Um" as a prefix used to denote change and is different than the stand alone meaning of "um."

So without checking with Hansel and Gretel, I'd bet a lot that "umlaut" refers to a "modified vowel" ("selbstluat"), since umlauts are only ever modified vowels.