When connecting/adding a League of Legends account to Challengermode, you need to type in the Summoner name, not the League of Legends account Username. Make sure that you are using your account's Summoner name, which can be seen in the top-right corner of the in-game client:
In League of Legends, there's a difference between your Summoner name and your League of Legends account (username):
"Your Username is what is used to log into your [League of Legends] account, both on the website and in the client. [...] Please note that this name cannot be changed.
Your Summoner Name is what your friends will see in-game. This is the name that you will be known by on screen and on your friends' buddy lists. Unlike usernames, your summoner name can be changed whenever you like."
See the full Summoner FAQ on Riot's support page.