AFAIK there was nothing beyond "Seres" that they knew of. China was essentially well known to the Romans as a source of silk, but it was geographically very vaguely represented on maps such as Ptolmey's map. I think it's highly unlikely any Roman had any specific knowledge of Korea or Japan given these circumstances, and if there was any information it would have been lumped together with the rest of their knowledge of "Seres". So, it would have been, to them, just another part of the "mysterious east." I don't think there's any specific evidence Romans knew about those countries.