Q1: Why don't you rename this article 2023 Türkiye–Syria earthquake, the official name for the first listed country?

A1: Because the English-language Wikipedia has a WP:COMMONNAME policy. We use names for countries and places that are the names commonly used for them in English, regardless of what official organizations use. Technically, this kind of name is known as an exonym. For example, we use the name Germany, instead of the native endonym Deutschland.

If or when that general English-language usage changes (as has happened in the past with place names such as Mumbai and Beijing), the same WP:COMMONNAME policy implies that the English-language Wikipedia will necessarily also follow suit. So far, that hasn't happened.

This has been discussed many times at Talk:Turkey, with the same result every time because of the common name policy; there is currently a moratorium at Talk:Turkey on further requests for name changes until 1 December 2023. Until that article is moved, this article will use Turkey in the article.