The "Order" designation may derive from the British honors system, or the Order of Merit awarded by the French Republic. The name "Karagite Order of Heroism" suggests the "Karagite" people or government may have awarded Kirk with a knighthood (or something similar) for actions on their behalf.
For the remastered episode of "Future Imperfect", the original Okudagram of Riker's service record was replaced by a new graphic. This award was mentioned in that graphic. The word karagite is spelled "kragite".