Name Pronunciation with Apostrophes

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

Other than O'Malley, the names in the question are most likely modern (Black) American names. Recently coined names can have unexpected pronunciations, and it's often safest just to ask the individual how to say the name.

That said, the apostrophe is most likely serving as purely a syllable-break mark in all three cases, and should not be "pronounced" itself (as an extra vowel).

I would expect both D'Andre and De'Andre to most likely be pronounced dee-AHN-dray, or possibly day-AHN-dray for the De' version, and La'Quanda to be luh-KWAHN-duh or lah-KWAHN-duh. (I can try to convert that to IPA if necessary, but hopefully this notation is sufficient for the OP.)

I haven't been able to find a good pronunciation guide for these modern coinages to describe what I think are somewhat common conventions, but I think this commentary by Steven Singer and the embedded video might be of interest to you.

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There seems to be some disbelief that these names are American, and should be read with different rules in mind than those of their (apparent) origins. I add some context in support of that view.

De'Andre, and its variant D'Andre, is actually a fairly common name in the US. It¹ first appeared in the top thousand in the early seventies, peaking in the mid-nineties when it was the 250th most commonly-bestowed name for baby boys in the US. As of 2015 it was still 610th. (See Behind the Name, or your favorite outlet for Social Security statistics). American sports fans might be familiar with NBA player DeAndre Jordan(or one of several other pro and elite college athletes with some form of the name), and enthusiasts in the UK might have heard of American DeAndre Yedlin, who plays for Newcastle United.

La'Quanda has never reached this level of popularity, but was given to at least 5 baby girls in the US in every year from 1969 to 2002. (Names.org)

Both names follow familiar naming patterns, combining popular elements taken from other languages in both the prefixes themselves and the use of the apostrophe in unexpected ways: in the case of De'Andre, by using the full de with the French name Andre where French would normally elide the e, and in the case of La'Quanda combining the article la with popular name elements -qua- and -a(w)nda.

From the linked article above (bolding mine):

Creating something new can be as simple as taking an Anglicized name and spelling it in inventive ways. Punctuation marks also can be utilized in unusual positions to add even more distinctiveness such as in the names Mo’nique and D’Andre.

At other times, they follow a cultural pattern to signify as uniquely African American using prefixes such as La/Le, Da/De, Ra/Re, or Ja/Je and suffixes such as -ique/iqua, -isha, and -aun/-awn.

And for the ultimate in creativity, try mixing and matching various influences and techniques. For instance, LaKeisha has elements from both French and African roots. Other names like LaTanisha, DeShawn, JaMarcus, DeAndre, and Shaniqua were created in the same way.

And just as the construction of these modern names follows some loose rules or patterns, so does their pronunciation. Most significantly for the OP's example, anything before an apostrophe should usually be pronounced as its own syllable, and stress is usually on the second syllable of the name.

I grew up with names like this; they seem fairly intuitive to me, but I know they can cause difficulties for the uninitiated, and I essentially never assume I know how to pronounce any particular individual's name. OP, after you have met more folks with names from this tradition they won't be as hard, but it still won't hurt to double-check.

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Edit: The popular Key and Peele video sketch "Substitute Teacher" shows some of these pronunciation conventions as applied to traditional Western names. YouTube video in link.

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¹ Note that the SS system strips out all punctuation and camel case, so De'Andre and DeAndre would both be counted along with Deandre. Similarly, La'Quanda only shows up as Laquanda.

According to the comments on BehindTheName.com, "De'Andre" is likely an alternative form of "DeAndre". Likewise, a search for "La'Quanda" seems to indicate it is a less popular spelling of "LaQuanda".

These names are African-American in origin, and do not necessarily follow the same rules as Irish or French names.

According to From Karen to Keisha: The New Black Names (emphasis mine):

Figlio’s third category of black names “include an apostrophe”. One could conjecture that the apostrophe might be confused with the French diacritical mark, the accent aigu which is used with eʹ. Perhaps the parents believe that this mark confers a high class status on the child. Some examples are: O’Shonda, Rog’Keisha, and Mi”qua (pronounced Miʹ quaʹ). The apostrophes have no apparent effect on the pronunciation, so one can guess that the function of the apostrophe is merely decorative.

I found an interesting post about this at BehindTheName.com, which also conjectures about the possible origins:

First, it comes partly from the existence of French, Italian, and Irish surnames that do use the apostrophe in their spelling. D'Amato, L'Hereux, O'Connor, etc. are just a few of the many examples of such surnames which occur in the United States. D'Andre, which was one of the first of these names to become popular in the African-American community, does exist as a French surname in that spelling.

The other large influence comes simply from a problem with the lack of use of diacritical marks in American typography... It was impossible, however, to put such marks on a birth certificate or other official forms. The closest you could get was to use an apostrophe instead. Andre', Mich'ele or Miche'le, and Rene'e are all examples of this, where the placement of the apostrophe seems to me to be an attempt to reproduce the French accent mark in the only way that was available at the time.

The meaning and origin of "quanda" seems questionable. Some sources claim it comes from Old English and means either "companion" or "queen." Considering how it came to America, I'm guessing it has something to do with creole languages that came out of South-Africa. Since "Queen" is not entirely uncommon as an African-American name for girls, that's probably it.

In any case, all of those types of names seem to come from various languages words for "of," "son of," or "the." In the "of" case (of, de, mac), it is a surname derived from adding "of" to an ancestor's name or place of origin. E.g.: O'Malley = Son Of Malley, Mc'Gleann = Of the Valley. For "the," (la, le) it would most likely denote an occupation or description of a person or their ancestor. E.G. L'Forge = The Blacksmith.

The apostrophe then stands in for the vowel; son of Gregor = mac Gregor = Mc'Gregor. American names that include the vowel AND the apostrophe are stylized, and there is no proper grammatical explanation, other than that two of Americans' favorite things are to "borrow" things from other languages and to be rebellious, making their own rules. It is simply a choice to keep both the vowel and the apostrophe, which in technical terms is unnecessary and does nothing to the pronunciation of it as a word.

In theory, it would be pronounced the same, but in practice, people who make such alterations to names are already straying from grammatical standards, so you can't be sure how to pronounce it without asking. In the end, names are a legal function that the owner has control over (to an extent). The point being, I could legally change my name to a smiley face emoji and say that it's pronounced "Lord Of Avalon," and it would be legally binding.