| Think about it. Vulcans, Romulans, the Klingon home world Kronos are all named after Earth's* Greek myths. Other names of races that are clearly of English origin include Bynars, The Founders, and The Dominion.
The answer to this weirdness? They speak English in Star Trek. The universal translates the Vulcan term for Vulcans and the planet Vulcan to the English term for Vulcans and the planet Vulcan just as you'd expect it to translate Deutschland to Germany.
This still leaves one problem: the Klingon pronunciation (in the Klingon language, that is) for Qo'noS (also spelt "Kronos") is the same as the English word Kronos. That is one oddity.
Another thing to consider, in the case of the Romulans there are two home worlds: Remus and Romulus. The planet name Romulus and the race name Romulan are both derived from the name of their original leader, Admiral Romulus. (Remember, the Romulans split off from the Vulcan Race around 300ad.)
While I'm rambling, most of the non-major races aren't named after their home worlds. In TOS they'd name the planet and then discover a(n English speaking) race living on the planet and the UFP would keep the same name for the planet and use the race's own name for the new race.
Oh, yeah. And the Borg speak Latin.
*Unless you consider Who Mourns for Adonis? (TOS) to make them not Earth-based. | 
