The question of how are wars named comes up quite often. Let's take a look at how naming conventions for wars and military conflicts has worked throughout history.
The naming wars and conflicts are a hodgepodge of conventions and methods. While the names of most wars (or at least the names that stick and are put into history books and school textbooks) change with time, there are several basic methods that have been used in history.
1. Name the war after your enemy: Examples include the Boer Wars, the Apache Wars, the Yaqui War, and so on. A popular term in Britain for that war where they lost the American colonies was "The American War." In Vietnam, the Vietnamese wars against foreigners from the 1940s to the 1970s are called, respectively, the French War, and the American War. Note that these war names reflect the who the enemy was, and, obviously, are not widely used in other countries. The Romans liked to name their conflicts this way, as in the Jewish Revolt, and the Punic Wars ("Punic" was the Latin word for Phoenician; the Roman foe, Carthage, was founded by Phoenicians).2. Name the war after the two main combatants: Many examples exist of this convention, as we see with the Mexican-American War, the Spanish-American War, various Anglo-French wars, the Franco-Prussian War, and the Russo-Japanese War.
2a. A subset of this naming convention would cover a naming a series of wars connected by the same belligerents. The Arab-Israeli Wars, the Anglo-French Wars, the Russo-Polish Wars are serial conflicts fought over sometimes very large spans of time between nations almost continually in conflict with each other. Within each series of wars are smaller conflicts with unique names, such as, in the Arab-Israeli example, the Six-Day War, the War of Attrition, the Yom Kippur War/Ramadan War, or the Lebanon War. Note that most of these wars are named according to other listed conventions.3. Name the war after the location in which it occurred: Geographic names are handy, in that it places the war in a certain spot in the world, and is popular also in that it is easier to use when there are multiple belligerents on both sides (or multiple sides, as often happens). Examples include the Korean War, the Vietnam War, the Gulf War, and the Crimean War.
4. Name the war for the cause of the conflict: While the causes of wars are not always obvious, sometimes the main reason for the war is clear enough to use in the name. The War of the Spanish Succession, or other "Succession" wars (Austrian, Polish, etc.) are clear; these wars were fought over who would claim power, or "Succeed" to the thrones of the various nations. Sometimes, the public reason for a war, such as when the Spanish cut off the ear of a British sailor named Jenkins led to that Anglo-Spanish war being called the War of Jenkins' Ear.
4a. The mirror image of this naming convention would be naming the war after the result of the war: Wars of independence fit well into this category. The American War of Independence, the Algerian War of Independence, and so on.5. Name the war for a leader in the war: The most well-known example is the series of wars called the Napoleonic Wars. While this is not the name of a single war, the wars waged by Napoleon is a handy and accurate name for a string of wars involving the diminutive French leader. Other examples include the Bar Kohba revolt in ancient Israel, and the American colonial conflicts known in the British colonies as Queen Anne's War, and King William's War. This also works for a war having a "nickname" as it were. The American Civil War is sometimes referred to as "Mr. Lincoln's War," while American participation in World War One is sometimes called "Mr. Wilson's War," after President Woodrow Wilson.
6. Name the war for a time period or year: Not used for modern wars very much, and definitely these names often were created by historians after the fact. The best-known examples include the Hundred Years War, the Thirty Years War, and the Six-Day War. Also, the War of 1812 fits into this category.
7. Name the war after a unique feature or aspect of the war: Many of the big wars are named this way: World War One, World War Two, and the Cold War among them. The world wars clearly encompassed most of the nations and regions of the world, and the Cold War was unique in that the main belligerents (Americans and the Soviets) never officially fought, and was the opposite of a "hot war."
8. Naming a war after the type of war: This one can be complicated, as it depends on the point of view. Words appended to a nation's name or location to describe the war include; rebellion, insurrection. revolt, revolution, uprising, intervention, coup, and border, among others. Also in this category would be civil wars. Examples include the Philippine Insurrection, the Boxer Rebellion, and the Russian Revolution.
Again, these descriptors are controversial, as the terms used change over time, and are dependent on whose side the observer favors. For example, the American Civil War has been called (often by those involved in the war, but also afterwards), as the War of the Rebellion, the War Between the States, the War of Northern Aggression, the Brothers War, and the War of the Secession, among others.
9. Naming the war with an operational code: In modern times, wars, campaigns, and battles are given official designations by the governments waging the wars. Operation Desert Storm (i.e. the Gulf War to Americans), Operation Iraqi Freedom (i.e. the Iraq War to Americans, Opération Licorne (Operation Unicorn, for the French intervention in the Ivorian Civil War), or Operation Palliser (British intervention in the Sierra Leone Civil War).
10. Naming the war for propaganda purposes: Actually, to a degree, many of the other naming conventions also fall into this category, though certain war names are more clearly propaganda-related than others. The Soviets/Russians referred to their participation in World War Two as "The Great Patriotic War," and the United States started out referring to the wars and battles against al-Qaida, the Taliban, Iraq, and others as "The Global War on Terror."
Humans like to categorize and name things, and wars and military conflicts are no exception. When you come across a war in reading or viewing historical or even current events, keep in mind that what it is called now, has likely changed over time, and, in reality, will change again. Yesterday's Great War became the First World War. Today's Global War on Terror will likely be called something else a generation or two from now.
Links:
http://mentalfloss.com/article/28711/how-military-operations-get-their-code-names
https://history.army.mil/reference/CODE.HTM
Joseph, P. (Ed.) (2017). The SAGE encyclopedia of war: Social science perspectives (Vols. 1-4). Thousand Oaks,, CA: SAGE Publications Ltd. doi: 10.4135/9781483359878