I suppose it's the Anglicized version, or the way these characters think of themselves.
But if they don't have any ability to vocalize and so no verbal language at all, then they wouldn't think in phonetics to begin with. Deaf people that have been deaf from birth but that know sign, for example, don't have an inner monologue in sounds at all, but in sign, because they have no conception of sound to have an inner monologue in. When they think to themselves, it's literally in sign.
So, like, a poetic name could make sense, something that was more a direct translation of the concepts that they associate to their species in the same manner as a name, but there would literally be no collection of sounds to Anglicize, so you couldn't have an otherwise-meaningless word like "Horta" as their name. It would actually make more sense if Spock had said they were called "the Children of the Stone" or something more metaphorical. (And this is assuming that they even have anything akin to a name at all, rather than just an abstract thought that has no meaning other than that it's the mental identification of their race or themselves as an individual.)
Edit: Oh, I found the thread. It's not about how names are chosen, though, but rather what naming conventions had been established for various Trek species, so I'm not sure it's actually relevant to you at all honestly. Just in case, though, here it is: http://www.trekbbs.com/threads/naming-conventions.266779/