Took me a while with that, too. I thought Odium was the person who held the Shard, because I had no idea it was actually a word. It means Hatred, essentially. I'm quite afraid.
Well, the discrepancy comes from the Shards not remembering their name, as I explained here http://www.17thshard.com/forum/index.php/topic,73.0.html The person who wrote the missive and its recipient, however, do know their names.
I, however, am quite certain that Rayse holds Odium.