Why some countries have more than one name?

A lot of variation in country names is based on translations. For instance, "Netherlands" means "Low Countries" and is called, in French, "Pays-Bas" which has the same meaning, but looks significantly different. It shall be noted that the United Nations has six official languages into which most UN documents are translated; therefore, though each UN member decides on its own name, it has to provide (at least) six variants for these six languages. Since these languages use widely different signs, one of them (Chinese) being non-alphabetic, a country cannot, logically, have a single official name valid worldwide.

Beyond translations, it so happens that countries may change names, and the new name is not necessarily adopted immediately and worldwide. For instance, in 1989, Burma changed its name to "Republic of the Union of Myanmar", shortened to "Myanmar", but many countries refused to recognize the legitimacy of the government of Burma (a military dictatorship), hence its ability to change the formal name of the country. As a UN member, the official English version of the country name is still "Myanmar", but "Burma" remains in wide usage in some other countries. For instance, this official document from the Australian government can be seen to use both "Burma" and "Myanmar" as country name, sometimes switching within the same paragraph with no explanation.

Country names have a huge symbolic value and can lead to interferences with and from other countries. Case in point: Macedonia (in the UN, Macedonia is known as "the former Yugoslav Republic of Macedonia", a name which is officially "provisional" and has been so for more than two decades).

Some countries have a "second" name that is derived from its most famous state or province. For instance, "Holland" is the most famous province of the Netherlands, Farsi (Persia) of Iran, etc. "Schweiz" or "Switzerland" is the most famous state of a country whose official name is the "Confederation of Helvetia."

"Germany," in its English form, was named after a group of "Germans," as was Aleman (Alemani). But the country's "real" name, in its native language, is "Deutschland."

There are many Geo political reasons for that. Most of the other names are kept by other countries. India is called India (from Indus) because British kept it. Its called Hindustan (Land of Hindus) because Arabs kept it. Germans call their country Deutschland but internationally it is called as Germany. It is the same as we have synonyms in any language for a word. If you consider Japan, they call it Nippon meaning Land of rising sun. So these different meanings give a country multiple names.

Historically, every country had many different names - what they called themselves, and what others called them. Conquerors came and said "This is now SomethingLand" while the people who lived there were already calling it "OurIsland" in their language or "LandOfTrees" in their language or whatever. [There is a claim that "Canada" comes from an Iroquoian word for "the village" because someone asked a guide "what do you call all of this place?" - it might not be true though.] Some folks called their neighbours Outsiders and their homes Outside, while those outsiders called themselves something different.

These days we're usually polite and call countries what they want to be called. But even that can be complicated. There is the province thing (this gives you not only Holland for the Netherlands, but England for the UK) but there is also the matter of abbreviations. Do you say the US or the USA or America?

In the end, there are a number of different words for "the Netherlands" in 10 different languages for exactly the same reason there are a number of different words for "cat" or "contract." They are different languages.