Probably not very much, there isn't really a market for usernames like in Runescape. I could see you getting 20 bucks if you found someone who really wanted it but it isn't worth the effort and cost of name change.
Didn't realize Watch was a player. IMO it will still be difficult to find the right buyer but it's probably worth a bit more than 20. People pay a lot for dumb stuff in league.
I didn't even know league had a username market, this is my first one seeing it. Sounds unique though so I'd expect atleast $30 but idk market for usernames on lol