Funny sort of name. Who would think of calling a little newborn baby Muriel?.
Some literature uses a diaeresis over the e to show that it is pronounced: so Bronte, Terpsichore, Hermione, could be written as Brontë, Terpsichorë, Hermionë, but since diaereses take effort to put in there on English keyboards, writers typically leave out the optional, yet helpful, diacritical mark. I think Hermionë is a rather learnèd girl and will decide to use the diaeresis when writing her name; when people ask why, it will give her opportunity to say “So you’ll pronounce my name correctly, ninny.”.