I have seen people refer to this site as "TeX.SE" and "TeX.SX". Which is more common? Is one preferred (by appearing in official places)?
I don't think that standardization is necessary: usage will sort it out. Nonetheless, it might be interesting to document the difference, possibly in relation to usage on/for other Stack Exchange sites.
The 'official' position across the network is to use 'SE', so that is what I use when talking to people on other sites. However, 'SE' is the TLD for Sweden, and 'SX' (or 'sx') fits nicely with 'TeX'. So on the site I and many others use a variation of 'TeX-sx' (TeX-SX, TeX.SX, etc.).
I strongly prefer "TeX-SX" to "TeX.SE" (note the punctuation) and "TeX.SX" is acceptable. I'd rather annoy random other StackExchange users than the Swedes. However, as this has brought it to my attention, I'd rather make the essential details of the site clear right at the outset: that it is about TeX and is hosted on the StackExchange network. Someone visiting the FAQ is more likely to be completely new to the SE network than just visiting from some other site. All of "TeX-SX", "TeX.SX" (is it some new variety of "FX"?), and "TeX.SE" (what has Sweden ever done to you?), are unclear on first sight (and site).
I've been using (and seeing other people use) »TeX.SE« for about two years now, and it never made me think of Sweden, until you mentioned it -- which is probably because domain names are hardly ever spelt in uppercase (and which is why I think it's important to keep spelling it that way). Both »TeX.SE« and »TeX.SX«, however, make me think of straight edge hardcore punk, but that's okay. I prefer ».SE« because it's more down-to-earth than ».SX« which I find too fancy, or to 1990s, probably because of that »FX« association:
SE. Why go against the norm?