As someone with a curiosity for foibles in language this one has puzzled me for a while - actually two things puzzle me.
Firstly in words like naïve and Noël where it denotes that the vowels should be pronounced as two separate vowels - is this a diaeresis or is this a tréma?
I think the German umlaut is a bit different as it actually changes the sound of the vowel (and sometimes the meaning of the word too).
Secondly is this a dead practice. Is it correct or incorrect for example to type coöperate, or zoölogical, or even reëlect. I did a little digging and most publications don’t use it any more but the New Yorker magazine does.
So.......over to the mighty brains and linguists of the Tz parish for the definitive answer.
So we are still waiting for the brains of the parish then
One thing's for sure, there's no definitive answer to matters of language usage, since it changes and evolves constantly (if rarely for the better).
Sadly, this diacritical has gone the way of the dipthong - lost through a mix of poor education and the limitations of the computer keyboard, though it may continue to jostle with the umlaut on heavy metal album covers in much the same abusive relationship that grocers have with apostrophes...
I won't elaborate on the finer points but both spelling come directly from French. Which itself took it from the Ancient Greek. And indeed, it means that the vowel is pronounced separately. Tréma is the name of the accent for us; Diaeresis (diérèse) is the effect of the accent, separating what would be a single syllable into two.
'Against stupidity, the gods themselves struggle in vain' - Schiller.
I don't think that there is any "Tréma...in English". It's not in the OED or Merriam Wester. But it is Larousse...link.
As for "coöperate, or zoölogical, or even reëlect", I'd go with the OED:
- co-operate
- zoological (although other versions are recognised "Forms: 17– zoological, 18 zöological, 18– zoölogical)
- re-elect
Then, the OP might like to use 'nowell' to get around his dilemma.
I only studied languages to GCSE but I would have though re-elect and co-operate are different because they are words with prefixes and I believe it was American english that did away with the hyphen. In comparison Noel was never No-el.
Good luck with persuading the OED about that (#8)...