Robert Comsol wrote:
A friend of mine from Australia who's very knowledgable about navy vessels in real life told me that the "Mark / MK" designation is exclusively used for devices (like the photon torpedos in ST) but never for naval vessels.
A brief Google search would seem to indicate that your Australian friend is either wrong or out of date. There would appear to be lots of ships with "Mark" or "Mk" designations. For example:
"The Mark V SOC
(Special Operations Craft) is a small marine security/patrol/transport boat manufactured by Halter Marine Inc. (Gulfport, Mississippi). The Mark V is one of the newest additions to the United States Naval Special Warfare Command."