In English specifically, the diaeresis is sometimes put on a final E that’s supposed to be pronounced and not silent. This started in transcriptions of Ancient Greek (“Eurydicë” doesn’t rhyme with “dice”, or “Persephonë” with “phone”), and then Tolkien used it for a bunch of his fantasy names for the same reason. But the most famous instance of it is probably the Brontë family—in the 1800s, Patrick Brontë (father of Charlotte and Emily) changed his name to the Ancient Greek word for “thunder”, and used the Ë to make sure people didn’t pronounce it like “bront”.
So I would read Amë as “ah-may” /a.me/ or “ay-mee” /ej.mi/ rather than “aim” /ejm/.
Is it permissible at this time to ask the author how in their minds they imagine the umlaut-ed name is to be pronounced? Because otherwise I will have to slow down each time I come across it and take one of 3 guesses, and never being able to settle on any particular one will make me additively cranky. ↩︎