It’s a Diaeresis (diacritic) or tréma, so named because it divides up two vowel letters to be pronounced as two syllables, which would otherwise be pronounced together as a single syllable (and typically a single vowel). So Zoë is pronounced Zo-ee, as distinct from rhyming with Joe.
It looks identical to the Germanic umlaut, but the umlaut is used to change the pronunciation of a vowel, and historically derived from a small <e>. The diaeresis OTOH has been two dots since it was invented for Hellenistic Greek.