The New Yorker is kind of well known for being virtually the only significant English publication which uses a diaeresis (the ¨) where almost everyone else uses a hyphen or just two repeated letters [0].
The diaeresis and umlaut are literally exactly the same Unicode character and the symbol or diacritic itself can be called either. The difference is what it does to the vowel — it’s a diaeresis if it indicates a repeated vowel, and an umlaut if it modifies the vowel sound.