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I wonder which form(s) are correct amongst the following:

I have also read some documents that added a diaeresis on the i, i.e. Naïve Bayes or naïve Bayes, probably reflecting the French etymology of the adjective naive.

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All the forms are commonly used:, it probably depends rather on each writer's personal style and on the style guide of the publisher of the text where the phrase appeared.

Bayes is always capitalized since it is a surname.

"naive" is or is not capitalized depending on a writer's style. It could be capitalized if a writer capitalizes all names of methods (e.g. Tom Michell, quoted by you, seems to capitalize also "Maximum a Posteriori", or "Maximum Likelihood Estimation"). It could be lowercase if all names are written lowercase (see similar example of distributions names). "Naïve" is just a alternative spelling for "naive" so it is just a question of spelling convention used by the writer.

See also https://english.stackexchange.com/questions/14/which-words-in-a-title-should-be-capitalized and https://english.stackexchange.com/questions/6560/when-should-you-use-title-case

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    $\begingroup$ I've edited for style. I've left unedited your comment on Bayes. Strictly, it's not correct that Bayes is always capitalized as I've often seen it all lower case. I agree personally that it's better to capitalize it. But words based on personal names can become accepted over time as all lower case. I'd not seen any one suggest that we are wrong to write "boycott".although the word comes from a person called Boycott. $\endgroup$
    – Nick Cox
    Commented Jan 4, 2016 at 1:13

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