Do any Capital cities have the same name as their country?

Yes. There are several countries whose capital cities share the same name as the country. Here are a few examples:

* Vatican City: The capital of Vatican City is Vatican City.

* San Marino: The capital of San Marino is San Marino.

* Mexico City: The capital of Mexico is Mexico City.

* Guatemala City: The capital of Guatemala is Guatemala City.

* Pretoria: The capital of South Africa is Pretoria.

* Maseru: The capital of Lesotho is Maseru.

* Bandar Seri Begawan: The capital of Brunei is Bandar Seri Begawan.

* Port Louis: The capital of Mauritius is Port Louis.

* Dodoma: The capital of Tanzania is Dodoma.

* Lilongwe: The capital of Malawi is Lilongwe.