I'm not sure I understand the situation correctly. Did you follow DTN's sticky at the top of the page? It's worked like a charm for me!
If you Blocked them they should certainly appear on the list. I just now tried DTN's method to test it and it worked fine for me. I was able to see the player's name that I blocked immediately, and was able to remove them with a click. Perhaps restart your client if it's not working.
If they're not on the Block list then they're not Blocked and you will still be able to see their messages and mastery emotes in-game.
Perhaps there is a bug in the system, though. Does the name have any special character or anything associated with it? I'd definitely recommend sending in a ticket to Support and/or use the Bug Report option in the bottom-right of the new client if you can't get it working with restarting the client and other minor troubleshooting. It could be something stuck on their end if the player has an awkward name (something like: 피자 애호가) might not show up due to us having an NA Client without the Korean Letter Packs. Likewise, Riot can probably assist you with something like that.
Best of luck OP, hope it gets resolved fast!