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.
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.
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.
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.