Which countries have the same name as their capitals?

Vatican City

https://en.wikipedia.org/wiki/Vatican_City#Crime

Brazil.

Brasília was built so that the federal capital of Brazil could be transferred from the coast to the Midwestern interior of the country. The name "Brasilia" comes from Latin and means "Brazil".

https://en.wikipedia.org/wiki/Bras%C3%ADlia

Djibouti. https://en.wikipedia.org/wiki/Djibouti
Guatemala. Guatemala City. https://en.wikipedia.org/wiki/Guatemala
Guinea-Bissau. Bissau ... upon independence, the name of its capital, Bissau, was added to the country's name to prevent confusion with the Republic of Guinea. https://en.wikipedia.org/wiki/Guinea-bissau

El Salvador. San Salvador. https://en.wikipedia.org/wiki/El_salvador
Luxembourg. https://en.wikipedia.org/wiki/Luxembourg
Mexico. Mexico City. https://en.wikipedia.org/wiki/Mexico
San Marino. https://en.wikipedia.org/wiki/San_marino
São Tomé and Príncipe. São Tomé. https://en.wikipedia.org/wiki/São_Tomé_and_Pr%C3%ADncipe
Singapore. https://en.wikipedia.org/wiki/Singapore
Tunisia. Tunis. Its name is derived from the capital Tunis located in the north-east. https://en.wikipedia.org/wiki/Tunisia

Some capitals and countries have very similar names, often because one was based on the other- e.g. Brasilia/Brazil, and Algiers/Algeria. This could get very complicated, using all the different versions in the different languages used, both in those countries and from abroad, so I will confine myself to the names (short forms) used in English.

Identical capital/country (apart from adding "city" to distinguish between them):

Andorra
Djibouti
Guatemala
Kuwait
Luxembourg
Mexico
Monaco
Panama
San Marino
Singapore
Vatican City

Very similar or related, but not exactly the same:

Algiers/Algeria
Brasilia/Brazil
Santo Domingo/Dominican Republic
San Salvador/El Salvador
Bissau/Guinea-Bissau
São Tomé/São Tomé and Principe
Taipei/"Chinese Taipei" (a.k.a. Taiwan, a.k.a. Republic of China)
Tunis/Tunisia

Belize* (was named after the former capital of the colony of British Honduras, and its river, but a new capital, Belmopan, was established in 1970, prior to the colony name becoming Belize in 1973)

-see https://www.countries-ofthe-world.com/capitals-of-the-world.html