Well, the letters don't necessarily have to be acronyms (SSN doesn't literally stand for "submersible ship, nuclear" does it?). If you assume the registry numbers denote operator as well as class, "NCC" could be a code prefix for "Federation Starship." The same ship, sold to a civilian contractor or the Vulcan Science Academy, for example, might have its prefix changed to "NCR" or "NGR" or what have you. You might take a clue from this from DS9, "The Siege of AR-558". Apparently this is supposed to be the name of the planet, but one might speculate that "AR" is a Federation prefix for a communications unit where "NAR" would be a communications vessel--a courier ship or similar type--and that "558" was simply a code indication for this particular junction.
Basically, the only registries we see are "NCC" because all the ships that have visible registries are all Starfleet vessels under Federal jurisdiction. I would bet that local starfleets--Andorian and Vulcan ships, for example--probably have different prefixes, standardized under some Federation regulation.