Diaereses, like umlauts, are diacritical marks consisting of two horizontal dots. Unlike umlauts, though, which alter a vowel’s standard sound, diaereses remind that the second of two adjacent vowels must be pronounced separately from the first. The names Chloë and Zoë, written here each with a diaeresis, rhyme with Bowie, yet without a diaeresis, Chloe and Zoe, according to our rules of pronunciation, should rhyme with doe.
With the exception of naïve, modern English has largely forgotten the diaeresis. Most words that once used a diaeresis—coöperate, reënact, zoölogy—are now written either plain (cooperate) or hyphenated (co-operate). Only The New Yorker, as its idiosyncrasy demands, requires its writers to use diaereses. All other writers should prefer the plain rendering shown in modern dictionaries.