... is not a British Overseas Territory in its own right; it's part of the British Overseas Territory of Saint Helena, Ascension and Tristan da Cunha.
The capital of the territory is Jamestown (population 630 in 2016), which is on St. Helena. Tristan da Cunha doesn't really have a capital, but Edinburgh of the Seven Seas (population 250 in October 2018) is its main settlement.
Edinburgh of the Seven Seas was named in honour of a visit made by Prince Alfred, Duke of Edinburgh, the second son of Queen Victoria, in 1867. According to Wikipedia, it's known locally as simply The Settlement or The Village.
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