This is a good question! I will post my view here, but I would be glad to hear others as well. As always, I'm happy to go forward with a community decision, whether I agree with it or not.
My suggestion is to keep the site name as it is for the following reasons:
- Latin is the main topic of the site, and anything having to do with Latin is on topic. (This may be overly simplified, but this is my starting point to our scope.)
- Simplicity is good, and the current site name is simple and informative.
- We allow some Greek, not all Greek. If we Greek were to be added to the title, then we might want to add some qualifiers. "Latin and Ancient Greek Stack Exchange" might work. The key words in your quote are "but not unconditionally". I am pretty sure our community does not want modern Greek.
- As on many SE sites, we can implicitly understand "Latin Language SE" to mean "Latin Language and Closely Related Topics SE". I prefer this level of specificity, so that we are free to redefine our scope.
- What about other languages? Should we add other Italic languages to the title as well? The name can't be a full description of the scope.
- I don't think we can change names often. If a good Greek site arises, perhaps many of our users might feel that Greek questions should be directed there in the future.
Please take these as thoughts in favor of the current name, not as hard facts. My main argument is that Latin is included unconditionally, Greek only conditionally.
For the sake of clarity of interpreting votes, let me post a second answer addressing "Classics" as a name.
I do not want to change the name to "Classical Languages SE" or "Classics SE". The reason is that in my opinion (and vision) all things Latin should be on topic. A name focused on the classical aspects may scare away medievalists or living Latin folks.
I will not try to hide that my interests are mainly in Latin and not other languages regarded as classical. (I might not be able to afford such a narrow interest if I was professionally engaged with Latin, but my field of scholarship is something unrelated and Latin is mostly a hobby.)
However, a combination like "Latin and Classics SE" would avoid this pitfall. Perhaps that could be a reasonable name? It is not immediately clear what is included in "Classics". But names don't have to be definitive; we can specify the details elsewhere.
Even just adding "Classics" to the title is a major change in my opinion. It shifts the focus somewhat from what we started with, and I find that significant. It is not just a matter of names, but a redefinition of purpose. Therefore I am against hasty movements, but not against all movement. If this suggestion gains significant support and very little opposition, I am ready to go forward and discuss such changes with SE staff. I can't tell what the next steps could be without such consultation.
Personally, I am slightly against this idea, but I could live with it. This is the most reasonable way to change the name I could think of, so I am posting it for others to judge.
For the sake of discussion, I'm going to post an alternative answer, though I do agree with everything Joonas said.
How about changing the name to Classical Languages SE or Classics SE? That neatly encompasses Latin, Ancient Greek, Etruscan, Sabellic, and the various lesser-known languages that get discussed here, while excluding post-classical Greek and the Romance languages.