On TNG, DS9 and VOY the Starfleet crews are primarily human with some sporadic representation of other races. Ds9 sort of breaks the mold but they had to as the show was set at Bajor and they had to have Bajorans outnumber everyone else put together. Even then, the Bajorans are Bajoran Militia and not Starfleet.
So why? The answer is that, even in the 24th century, Starfleet is still largely a human organization.
Benzar was a very important world in the Federation and it was devastating when the Dominion conquered it during the war. However, Mordock was the first Benzite to go to Starfleet Academy at the same time Wesley Crusher was taking his (first round of) entrance exams. Meanwhile, Mendon served on board the Enterprise as part of an officer exchange and referenced protocol on board a Benzite ship in A Matter of Honor. That indicates that at least some Federation members maintain their own fleets and or militaries.
The idea of other fleets/militaries inside the Federation is further implied in Unification when Vulcan ships are used to conceal a Romulan invasion of Vulcan and in Gambit when T'Paal poses as a member of Vulcan (not Starfleet) Intelligence. While the ships could be science or military (or any other kind of) vessels and it's never stated on screen it is clear that Vulcan maintains its own fleet and it's further clear that not ALL of the security of Vulcan has been integrated into Starfleet.
Finally, in the Dauphin, when asked what species is aboard the Enterprise, Picard promptly responds with human. That at least implies that he considers his crew to be primarily human (which we see is true through the course of the series).
So if Starfleet is primarily Human, then it would make sense to use Earth centric names.
Edit: I realized that I didn't answer the question that was asked.
Specifically, the OP asked if there were examples, other than the T'Kumbra, of Starfleet ships with names based on non human cultures. The answer is probably and some were pointed out in a previous answer.
That said, as a predominantly human organization, a member, event, place of significance etc. in another culture would have to have a major impact on humanity, or the whole of Federation society to warrant its name being used on a Starfleet ship. For example, Kahless the Unforgettable (not the clone) was of major importance to the Klingons but had little, if any, impact on humanity or the Federation as a whole. That said, it's unlikely that there would ever be a USS Kahless. For the same reason, an IKS MacArthur would be equally unlikely.