I have no idea what those speckles are, they don't seem to be inside the stone, just on the surface, maybe its something not natural, something got sprayed on it or maybe its organic, try scrubbing it under hot water with a wire brush, the stone is blue grey Chalcedony/Agate, atleast I think I see light bands in the first picture which would make it an Agate but Chalcedony for sure.