If you're talking about live chess, I'm pretty sure you can block whichever player you want to but unfortunately it can be painfully difficult just to find the 'block' button sometimes. It's easier if you find their name on a list of some kind, e.g. a player list in a tournament.
For online chess, I don't think it's possible to do that but I'm not really sure to be honest, does anyone else know?
I have been playing against players that wont move when loosing, is it possible to block them afterwards?