Well Omega, being the last letter of the greek alphabet, is generally used to mean "the end", "the last" or "the ultimate limitation of ability" in epic situations. So whoever has that name is likely either the last of their kind (maybe a long lost insanely powerful race, like dragons), the highest possible evolution of their kind (or possibly the series of mutations/experiments that created them) or hellbent on bringing about the end of the world (such as a doomsday cult or an antichrist figure). Those are my thoughts.