(1) A diacritical mark (two dots
(2) A diacritical mark (two dots) placed over a vowel in German to indicate a change in sound [also: diaerses (pl)
(3) diaereses (pl)]
(1) The New Yorker is probably the last popular magazine in the English-speaking world where the editors insist on the diaeresis (not umlaut) in u251cu00f6u251cu00e7u251cu2510cu00d4u00f6u00a3u251cu00e9operateu251cu00f6u251cu00e7u251cu00fb.
(2) This misspelling had been tackled earlier by Chast, who pointed out that Laennec, a native of Brittany, did not write his name with a diaeresis in his publications.
(3) As several commenters have pointed out, both publications insist on using the diaeresis mark (as in nau00d4u00f6u00a3u252cu2557ve, for example) even though it hasn't been in common usage for several decades at least.
(4) No diacritic marks are normally used for native English words, unless the apostrophe and the diaeresis sign are counted as such.
umlaut
dieresis