Where did the names for today's countries originate from?

Names of nations come from a variety of sources and names provide a lot of clues about the culture. Central Asia and Eastern Europe names are mostly named after various tribes, providing an idea to the strength of historic tribes and the constant strive to balkanization / reuniting. 


African nations and Carribean are predominantly named after key rivers and natural resources - reflecting the fact that colonists were after the natural resources and most modern borders don't reflect ancient tribal boundaries. Americas have a few people names reflecting the importance of explorers/revolutionaries. Asian names are often very ancient names used by outsiders and often based on simple things.

Rivers

India is named after the river Indus (the original name is Sindhu, that has been corrupted to Indus by the Greeks). Republic of Congo & Democratic Republic of Congo are both named after river Congo. Niger and Nigeria are named after the river Niger. Zambia from Zambezi river. Uruguay, Paraguay, Jordan are other nations named from eponymous rivers.

People Names

This is common in Latin America and Oceania where explorers often left their name.

Americas and USA are named after the explorer Amerigo Vespucci, who conclusively showed that the land Columbus discovered was a new continent.  Colombia is from Christopher Columbus, Phillipines from Phillip II of Spain, Saudi Arabia from the house of Saud, Domican Republic from Saint Dominic, El Salvador  from Jesus (the Savior in Spanish), St. Lucia from Lucy, Mauritius fromMaurice (of Nassau) and Bolivia from Simon Bolivar (who liberated much of Latin America).

Laos comes from Lava - first son of King Rama (hero of Ramayana). (Sri Lanka is the other country named from Ramayana). India's second official name Bharatcomes from Emperor Bharata. Israel comes from the other name of the Biblical patriarch - Jacob. 

Ethnic Groups

This is very common Central Asia and Eastern Europe.
Somalia, Afghnistan, Mongolia, Thailand, Hungary, Germany Poland, Bangladesh, Iran, Armenia Kazhkstan, Turkey, Bulgaria, Bosnia, Belgium, Botswana, Albania, Burundi, Lesotho, Cambodia, Lithuania, Latvia, Czekhs, Slovaks are all from the tribal groups of the same name.

City names

This is primarily used in Middle East. Iraq is from the ancient city of Uruk. Tunisia comes from the city Tunis, Morrocco from the city of Marrakesh. Djibouti, Kuwait and Mexico are named after the eponymous cities. 

Aspirational names

This is sometimes used in countries that win freedom. Liberia is the land of the liberated slaves from North America. Liberia means the land of the freed. Pakistan split from India and named itself "land of the pure". Burkina Faso means land of honest men and Uzbekistan means the land of the free.

Names of Iceland and Greenland are  swapped. Greenland was named so to attract other settlers to that frigid land. Iceland was named so to detract other settlers from settling in their nice spot. 

Directions

Norway means north and Australia means south. Austria means the Eastern tribe (among the Germanic tribes) and Asia again means east (east of Greece). Vietnam meant southern kingdoms to distinguish from the kingdoms in the Chinese province of Guandong.  Japan means the "Land of the rising Sun" in Chinese (Japan is to the east of China)

Based on other countries

Romania was named after Ancient Rome, Indonesia as the land beyond India, Belarus means White Russian and South Sudan is the nation that split from Sudan on its south.

Other Geographic Features

This naming convention is quite common in Latin America. Brazil comes from the Brasilwood (meanign red wood in Portuguese). Costa Rica means a rich coast of gold and Ivory Coast from ivory trade. Jamaica meant "land of springs" and Haiti meant "land of mountains" in Arawak. Guyana means a land of many rivers and Panama means the land of many fishes in local languages.

Singapore means the city of lions in Sanskrit.