You may have noted words with two dots over a vowel in my writing. The mark is a dieresis, not an umlaut — they are two different diacritical marks. To my knowledge, only The New Yorker magazine still uses it (well, besides me). [Search for 'the curse of the dieresis New Yorker', as external links aren't permitted in blog entries which show up on the feed]
The dieresis is a generally deprecated way of indicating that a pair of consecutive vowels are not a diphthong. For printers, they generally substituted a hyphen to reduce the number of letters in their fonts, and eventually, hyphens mostly (but not completely) disappeared. Over time coöperate became co-operate then cooperate.
I have consistently used it in 'naïve' since day one, but over time have added others. I also still use diacritical marks on other words where most have dropped them (e.g. maître d'hôtel) and words where they are necessary for clarity (e.g. résumé for a CV; resume to restart something),
I also have a quirky style that mixes US English and International (aka 'British') English (e.g. using 'afterwards' and 'amongst' rather than 'afterward' and 'among' and using 'litre' and 'theatre' instead of the US-standard 'liter' and 'theater'). I also play around with archaic words such as 'baxter' (a female baker), and obscure words, such as 'canapé' (something you sit on, not something you eat).
English is a magnificent bastard tongue (as linguist John McWhorter has called it) and I like to make full use of it!