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Technically speaking, every country has a capital. The most likely country that could be referred to as having no capital is Vatican City (in the centre of Rome, Italy) because the whole country (0.44 sqkm) is it's own city. Nauru also has no capital because it lacks any sizable population. However, most its leadership governs from the Yaren District.
Some other countries that have the same capital name as the country are:
San Marino (Europe)
Panama (Central America)