What does an apostrophe in a name mean? Examples: D'Artagnan - The Three Musketeers and F'lar - Dragonflight?

I don't know about Dragonflight, but D'Artagnan was a living person and the apostrophe means in French language usually a left out vowel. "De Artagnan"- From Artagnan.

The French language has a different system about vowels than the English language. So if most words end with a spoken vowel (usually e in the end), will lead to a shortened contraction bound by an apostrophe.

de Aria - d'Aria (from Aria) quelque un - quelqu'un - someone jusque à - jusqu'à - until ce est - c'est

It usually is used - as you can see - with "de", "ce" and "que" - which are often used in a sentence in the French language. Also, this is for a more fluent language when speaking, so the syntax keeps intact.

English language takes the contraction from the following word: I will - I'll I have - I've I am - I'm I had/I would - I'd