I found a dialog box on SE (all sites, not just this one) that capitalizes it as "TeX-LaTex Stack Exchange".
This seems odd to me, as Wikipedia uses a capital X in LaTeX. That said, I'm not super active on this site. The lack of spacing surrounding the hyphen also seemed odd. What is the preferred capitalization for the site name? Also, should there be spaces around the hyphen?
Bonus question: after reading this Meta post, what's the correct dash (or hyphen) to use in the site name?
Capitalization first. The "X" in "LaTeX" is definitely capitalized. First, it is based on "TeX"; second, that is the way it is rendered by LesLie Lamport in his definitive manual that launched LaTeX publicly. (What does the "La" represent? Leslie won't say, but he did say, at a DECUS meeting many years ago, that one could say "LayTeX" or "LahTeX", anything but "ELL Ay TeX".)
And why is the "X" capitalized? As explained by Knuth in Chapter 1 of The TeXbook, it is a roman-letter rendering of "tau epsilon chi". To make it distinct, the \TeX logo was created, with the lowered "E" to make it distinctive, and because "epsilon" is not a tall letter. (Nowhere is it explained clearly why the "T" is uppercase; perhaps because it's the initial letter of a proper name.)
An attempt was made by the AMS (the American Mathematical Society) to register this as a trademark. But Honeywell Information Systems, which had already registered "TEX" as a trademark for their "Text EXecutive processor", complained by means of a stern letter from their lawyers, insisting that the name be changed. But word got around in the computer science community, of which Honeywell was also a part, and the high level of community support for Knuth persuaded Honeywell to withdraw their demand. "TeX" was agreed as a compromise, as long as the "e" is lowercase in situations where it's not possible to render the actual logo.
Sadly, a number of bibliographic services and tools still don't manage to get this right. But anyone who knows the background can help by watching for correct usage and pointing out infractions when seeing them.
Regarding hyphens vs. dashes, I will agree with the answer to the cited question that endash is more appropriate than an emdash. I will avoid saying anything about the spaces.
Eis a reminder that TeX is about typesetting, and it distinguishes TeX\ from other system names. In fact, TEX (pronounced tecks is the admirable Text EXecutive processor developed by Honeywell Information Systems. Since these two system names are pronounced quite differently, they should also be spelled differently. The correct way to refer to TeX in a computer file, or when using some other medium that doesn't allow lowering of the `E', is to type TeX. Then there will be no confusion with similar names, and people will be primed to pronounce everything properly.