Ecuador is the name of a country. It is not a capital city of any country.
The country that has a capital city with the same name as the country and is the largest city in the world is Russia. The capital is Moscow, which is also the largest city in Russia.
The Mamphis in Egypt was once its capital.
Cairo is a city, the capital of modern Egypt. It is also the name of the province of Egypt that houses the capital city. (This is in much the same way that Madrid is both the name of the city and the province in which Madrid the city is located.)
Algeria is the country and its capital is Algiers.
Algeria has a capital city with a name that is not the same as the country. Algiers is the capital and largest city of Algeria. Panama City is the capital and largest city of the Republic of Panama. Djibouti City is the capital and largest city of Djibouti. Guatemala City is the capital and largest city of the Republic of Guatemala.
The small African country that shares the same name with its capital city is Djibouti.
Suva is the capital city in Fiji.
Tegucigalpa is the capital and largest city of Honduras, a country in Central America.
The capital city of the Basque Country is Vitoria-Gasteiz.
Cairo, Egypt.
Memphis