From an English perspective I have not come across this notation. However, the British monarchy do not have surnames per say, but rather belong to a "house".
If I had to speak this statement I would probably say:
Elizabeth the Second of the Royal House of Windsor.
The simplest answer to your question is that you should assume that if the apostrophe represents a missing letter, then that letter is not intended to be pronounced. Just treat the apostrophe as a slight pause.
The real problem with your question is that these are not English names and so it is hard to predict how they should be pronounced without knowing the original language. O'Malley is Irish, D'Andre is probably French and La'Quanda could be Italian.
As far as O'Malley is concerned, the spelling in Irish Gaelic is Ó Malley (descendent of Malley). I'm guessing that the acute accent on the letter Ó was transformed into an apostrophe for the convenience of English typesetters, but I may be wrong. In any case, there is no missing letter in this instance. Names from other languages need to be treated on a case by case basis.
Another problem is that as foreign names become established in the English language, their pronunciation can change from generation to generation even though the original spellings are retained. This can make it impossible for anyone to know how to pronounce some names without being told.
Two notorious examples (in BrE) are Cholmondeley and Featherstonhaugh. Both names derive from Old English. The first is pronounced chum-ley and the second is pronounced fan-shaw. Some owners have changed the spellings to make them more phonetic whilst others have insisted on keeping the ancient forms, possibly for their amusement at the confusion that it causes.
Wikipedia: Irish Names
Best Answer
The mark on the letter "ë" and other vowels like it can actually be one of two things:
In English, it is normally the latter:
Furthermore,
Here I'll add some IPA
For example, "Chloë" /kləʊ.i/ and "Zoë" /zəʊ.i/ do not rhyme with "toe" /təʊ/, even when written without a diacritic. They have two syllables (indicated by the
.
break in the IPA, which is a casual notation) compared to one.In American English (and I suspect other dialects, but I'm hesitant to say absolutely), they rhyme with "doughy" /ˈdoʊ.i/, as in: