Why do some countries have “the” in front of their names? For example: “The Netherlands” or “The Philippines.”

This isn't primarily a matter of history, but of, as you say, grammar.

"France," "Germany," "China", etc, are proper nouns, and so don't have a "the". Just like you wouldn't generally say "the Fred," or "the Sarah."

However, there are non-proper noun words in countries names. For example, "The United States of America," "The People's Republic of China", "The Kingdom of Spain," "The United Arab Emirates." You're not saying "The America," you're saying "The (adjective) States". Of course, you're using it as a proper noun (because it's the name of a country), hence the capital letter, but it's not a proper noun grammatically.

That's when we come to "the Netherlands." The Netherlands isn't, gramatically a proper noun like "France" or "Japan". It's just a synonym of "the Low Countries." Also, note the plural. Similarly, "the Virgin Islands," "the Bahamas," "the Philippines", which all are plurals; it's not one Bahama, it's a whole bunch of Bahamas (ie islands). Same with the Philippines, whose name is derived from the Spanish for "the Philippine islands" (Las Islas Filipinas)

The Gambia is called "the Gambia" because it's just named after the River Gambia. Congo is sometimes called the Congo for the same reason.

You may notice that sometimes English speakers call Ukraine, "The Ukraine." This is actually very contraversial: "Ukraine" means something like "border region." Calling it Ukraine implies it's the name of a country; calling it "The Ukraine" implies that it's the border region of another country (ie Russia). This is why the Ukrainian government has issued official advice to English speakers to please call the country "Ukraine" and not "The Ukraine".

You asked about other languages, and the answer is it's very variable, because use of articles (ie "a", "the," and "an" in English, as well as words like le/la, der/die/das and ein/eine/einen, etc) vary extensively between languages. German, Dutch and other Germanic languages tend to be somewhat similar. Russian has no articles whatsoever (so "Ukraine" vs "the Ukraine" is luckily not an issue). Chinese has preceding particles like "ge", but they're not really the same as articles, and are not used for countries ("The People's Republic of China", translated into Chinese and back again is just "People Republic China"). Filipino does have a definite article (ang), but while in English the government uses "The Philippines", in Filipino it's not "ang Pilipinas", but just "Pilipinas."

Sources: I can supply various English textbooks and academic works on English linguistics, but as I said, this isn't a historical issue, primarily. Except where whoever was there at the time called it X or The Y.