Learn English – What’s the right way to pronounce “Louis”

I think this is a mild hyperforeignism that comes from an attempt to pronounce “Naomi” more like the original Hebrew: nah-oh-mee [na.o.mi]. The [ao] sequence is uncommon in English—and because there are two separately stressed syllables in this case, they cannot merge into ow [aʊ]. Thus an epenthetic /y/ [j] sound appears, giving nah-yo-mee [na.joʊ.mi]. This is just like someone saying “drawring” instead of “drawing”: the transition between a certain pair of vowels is uncommon, so a consonant appears to simplify pronunciation.

The reason you hear it as nye-oh-mee then becomes clear: an [a] sound followed by a [j] sound approximates the regular English “long I”, which is in fact a diphthong, and not a single vowel. As a similar example, consider the word diode, which could be rendered as dye-ode [daɪ.oʊd], but also as dah-yode [da.joʊd].

So it’s a matter of principle: call your daughter by the name (pronunciation) she was given, but also acknowledge that neither pronunciation is really any more “right” than the other. If someone wants to name their daughter Naomi (or son, whatever, it’s a free country) but pronounce it “squeemdge”, then that’s their problem, and they’ll just have to correct people. Often.

You have to distinguish English vowels from English orthography. There are between twelve and fifteen distinct vowels in English, depending on your dialect, but there are only 5 vowel letters in the orthography. This causes no end of problems.

The letter æ was used in Old English to represent the vowel that's pronounced in Modern English ash, fan, happy, and last: /æ/. Mostly we now spell that vowel with the letter a, because of the Great Vowel Shift.

When æ appears in writing Modern English, it's meant to be a typographic variant of ae, and is pronounced the same as that sequence of vowel letters would be. So Encyclopaedia or Encyclopædia, no difference.